1.4: CHAPTER 3 ARISTOTELIAN VIRTUE ETHICS
Aristotelian Virtue Ethics
To seek virtue for the sake of reward is to dig for iron with a spade of gold. 1
1. Aristotelian Virtue Ethics Introduction
Aristotle (384–322 BC) was a scholar in disciplines such as ethics, metaphysics, biology and botany, amongst others. It is fitting, therefore, that his moral philosophy is based around assessing the broad characters of human beings rather than assessing singular acts in isolation. Indeed, this is what separates Aristotelian Virtue Ethics from both Utilitarianism and Kantian Ethics.
2. The Function Argument
Aristotle was a
teleologist
, a term related to, but not to be confused with, the label “teleological” as applied to normative ethical theories such as Utilitarianism. Aristotle was a teleologist because he believed that every object has what he referred to as a final cause. The Greek term
telos
refers to what we might call a purpose, goal, end or true final function of an object. Indeed, those of you studying Aristotle in units related to the Philosophy of Religion may recognise the link between Aristotle’s general teleological worldview and his study of ethics.
Aristotle claims that “…for all things that have a function or activity, the good and the ‘well’ is thought to reside in the function”.
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Aristotle’s claim is essentially that in achieving its function, goal or end, an object achieves its own good. Every object has this type of a true function and so every object has a way of achieving goodness. The telos of a chair, for example, may be to provide a seat and a chair is a good chair when it supports the curvature of the human bottom without collapsing under the strain. Equally, says Aristotle, what makes good sculptors, artists and flautists is the successful and appropriate performance of their functions as sculptors, artists and flautists.
This teleological (function and purpose) based worldview is the necessary backdrop to understanding Aristotle’s ethical reasoning. For, just as a chair has a true function or end, so
Aristotle believes human beings have a telos
. Aristotle identifies what the good for a human being is in virtue of working out what the function of a human being is, as per his Function Argument.
Function Argument
1. All objects have a
telos
.
2. An object is good when it properly secures its
telos
.
Given the above, hopefully these steps of the argument are clear so far. At this point, Aristotle directs his thinking towards human beings specifically.
3. The
telos
of a human being is to
reason
.
4. The good for a human being is, therefore, acting in accordance with reason.
In working out our true function, Aristotle looks to that feature that
separates man from other living animals
. According to Aristotle, what separates mankind from the rest of the world is our ability not only to reason but to
act on reasons
. Thus, just as the function of a chair can be derived from its
uniquely differentiating characteristic
, so the function of a human being is related to our uniquely differentiating characteristic and we achieve the good when we act in accordance with this true function or
telos
.
The notion that man has a true function may sound odd, particularly if you do not have a religious worldview of your own. However, to you especially Aristotle wrote that “…as eye, hand, foot and in general each of the parts evidently has a function, may one lay it down that man similarly has a function apart from all these?”
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On the basis that we would ascribe a function to our constituent parts — we know what makes a good kidney for example — so too Aristotle thinks it far from unreasonable that we have a function as a whole. Indeed, this may be plausible if we consider other objects. The component parts of a car, for example, have individual functions but a car itself, as a whole, has its own function that determines whether or not it is a good car.
3. Aristotelian Goodness
On the basis of the previous argument, the good life for a human being is achieved when we act in accordance with our
telos
. However, rather than leaving the concept of goodness as general and abstract we can say more specifically what the good for a human involves. Aristotle uses the Greek term
eudaimonia
to capture the state that we experience if we fully achieve a good life. According to Aristotle,
eudaimonia
is the state that all humans should aim for as it is the aim and end of human existence. To reach this state, we must ourselves act in accordance with reason. Properly understanding what Aristotle means by
eudaimonia
is crucial to understanding his Virtue Ethical moral position.
Eudaimonia
has been variously translated and no perfect translation has yet been identified. While all translations have their own issues,
eudaimonia understood as flourishing
is perhaps the most helpful translation and improves upon a simple translation of happiness. The following example may make this clearer.
| Naomi is an extremely talented pianist. Some days, she plays music that simply makes her happy, perhaps the tune from the television soap opera “Neighbours” or a rendition of “Twinkle, Twinkle Little Star”. On other days, she plays complex music such as the supremely difficult Chopin-Godowsky Études. These performances may also make Naomi happy, but she seems to be flourishing as a pianist only with the latter performances rather than the former. If we use the language of function, both performances make Naomi happy but she fulfils her function as a pianist (and is a good pianist) only when she flourishes with the works of greater complexity. |
Flourishing in life may make us happy but happiness itself is not necessarily well aligned with acting in accordance with our
telos
. Perhaps, if we prefer the term happiness as a translation for
eudaimonia
we mean really or
truly
happy, but it may be easier to stay with the understanding of
eudaimonia
as flourishing when describing the state of acting in accordance with our true function.
Aristotle concludes that a life is
eudaimon
(adjective of
eudaimonia
) when it involves “…the active exercise of the mind in conformity with perfect goodness or virtue”.
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Eudaimonia
is secured not as the result exercising of our physical or animalistic qualities but as the result of the exercise of our distinctly human rational and cognitive aspects.
4. Eudaimonia and Virtue
The quotation provided at the end of section three was the first direct reference to virtue in the explanatory sections of this chapter. With Aristotle’s theoretical presuppositions now laid out, we can begin to properly explain and evaluate his conception of the virtues and their link to moral thinking.
According to Aristotle,
virtues are character dispositions or personality traits
. This focus on our dispositions and our character, rather than our actions in isolation, is what earns Aristotelian Virtue Ethics the label of being an
agent-centred
moral theory rather than an
act-centred
moral theory.
Act-Centred Moral Theories
Utilitarianism and Kantian Ethics are two different examples of act-centred moral theories due to their focus on actions when it comes to making moral assessments and judgments. Act-centred moral theories may be teleological or deontological, absolutist or relativist, but they share a common worldview in that particular actions are bearers of moral value — either being right or wrong.
Agent-Centred Moral Theories
Aristotelian Virtue Ethics is an agent-centred theory in virtue of a primary focus on people and their characters rather than singular actions. For Aristotle, morality has more to do with the question “how should I
be
?” rather than “what should I
do
?” If we answer the first question then, as we see later in this chapter, the second question may begin to take care of itself. When explaining and evaluating Aristotelian Virtue Ethics you must keep in mind this focus on character rather than specific comments on the morality of actions.
Aristotle refers to virtues as character traits or psychological dispositions. Virtues are those particular dispositions that are appropriately related to the situation and, to link back to our function, encourage actions that are in accordance with reason. Again, a more concrete example will make clear how Aristotle identifies virtues in practice.
All of us, at one time or another, experience feelings of anger. For example, I may become angry when my step-son thoughtlessly eats through the remaining crisps without saving any for others, or he may feel anger when he has to wait an extra minute or two to be picked up at work because his step-father is juggling twenty-six different tasks and momentarily loses track of time (how totally unfair of him…). Anyway, as I was saying, back to Aristotle, “Anyone can become angry — that is easy. But to be angry with the right person, to the right degree, at the right time, for the right purpose, and in the right way — that is not easy”.
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For Aristotle,
virtue is not a feeling
itself but an appropriate psychological disposition in response to that feeling; the proper response. The correct response to a feeling is described as acting on the basis of the
Golden Mean
, a response that is neither excessive nor deficient. The table below makes this more apparent.
| Feeling/Emotion | Vice of Deficiency | Virtuous Disposition (Golden Mean) | Vice of Excess |
| Anger | Lack of spirit | Patience | Irascibility |
| Shame | Shyness | Modesty | Shamefulness |
| Fear | Cowardice | Courage | Rashness |
| Indignation | Spitefulness | Righteousness | Envy |
Anger is a feeling and therefore is neither a virtue nor a vice. However, the correct response to anger — the Golden Mean between two extremes — is patience, rather than a lack of spirit or irascibility. Virtues are not feelings, but characteristic dispositional responses that, when viewed holistically, define our characters and who we are.
The Golden Mean ought not to be viewed as suggesting that a virtuous disposition is always one that gives rise to a “middling” action. If someone puts their life on the line, when unarmed, in an attempt to stop a would-be terrorist attack, then their action may be rash rather than courageous. However, if armed with a heavy, blunt instrument their life-risking action may be courageously virtuous rather than rash. The Golden Mean is not to be understood as suggesting that we always act somewhere between complete inaction and breathless exuberance, but as suggesting that we act between the vices of excess and deficiency; such action may well involve extreme courage or
exceptional
patience.
In addition to feelings, Aristotle also suggests that we may virtuously respond to situations. He suggests the following examples.
| Situation | Vice of Deficiency | Virtuous Disposition (Golden Mean) | Vice of Excess |
| Social conduct | Cantankerousness | Friendliness | Self-serving flattery |
| Conversation | Boorishness | Wittiness | Buffoonery |
| Giving money | Stinginess | Generosity | Profligacy |
We must keep in mind the agent-centred nature of Aristotelian Virtue Ethics when considering these examples. A person does not cease to have a witty disposition in virtue of a single joke that might err on the side of buffoonery, or cease to be generous because they fail to donate to charity on one occasion. Our psychological dispositions, virtuous or not, are only to be assessed by judgment of a person’s general character and observation over more than single-act situations. If we act in accordance with reason and fulfil our function as human beings, our behaviour will generally reflect our virtuous personality traits and dispositions.
5. Developing the Virtues
In a quote widely attributed to Aristotle,
Will Durrant
(1885–1981) sums up the Aristotelian view by saying that “…we are what we repeatedly do. Excellence, then, is not an act but a habit”.
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It is fairly obvious that we cannot become excellent at something overnight. Making progress in any endeavour is always a journey that requires both effort and practice over time. Aristotle holds that the same is true for human beings attempting to develop their virtuous character traits in attempt to live the good life. You may feel yourself coming to an Aristotelian Virtue Ethical view after reading this chapter and therefore be moved to become wittier, more courageous and more generous but you cannot simply acquire these traits by decision; rather, you must live these traits in order to develop them.
Cultivating a virtuous character is something that happens by practice. Aristotle compares the development of the skill of virtue to the development of other skills. He says that “…men become builders by building” and “…we become just by doing just acts”.
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We might know that a brick must go into a particular place but we are good builders only when we know how to place that brick properly. Building requires practical skill and not merely intellectual knowledge and the same applies to developing virtuous character traits. Ethical characters are developed by practical learning and habitual action and not merely by intellectual teaching.
In the end, the virtuous individual will become comfortable in responding to feelings/situations virtuously just as the good builder becomes comfortable responding to the sight of various tools and a set of plans. A skilled builder will not need abstract reflection when it comes to knowing how to build a wall properly, and nor will a skilled cyclist need abstract reflection on how to balance his speed correctly as he goes around a corner.
Analogously, a person skilled in the virtues will not need abstract reflection when faced with a situation in which friendliness and generosity are possibilities; they will simply know on a more intuitive level how to act. This is not to say that builders, cyclists and virtuous people will not sometimes need to reflect specifically on what to do in abnormal or difficult situations (e.g. moral dilemmas, in the case of ethics) but in normal situations appropriate responses will be natural for those who are properly skilled.
It is the need to become skilled when developing virtuous character traits that leads Aristotle to suggest that becoming virtuous will require a lifetime of work. Putting up a single bookshelf does not make you a skilled builder any more than a single act of courage makes you a courageous and virtuous person. It is the repetition of skill that determines your status and the development of virtuous characters requires a lifetime of work rather than a single week at a Virtue Ethics Bootcamp.
6. Practical Wisdom (Phronesis)
Aristotle does offer some specifics regarding how exactly we might, to use a depressingly modern phrase, “upskill” in order to become more virtuous. Aristotle suggests that the aim of an action will be made clear by the relevant virtuous characteristic as revealed by the Golden Mean; for example, our aim in a situation may be to respond courageously or generously. It is by developing our skill of practical wisdom (translation of “
phronesis
”) that we become better at ascertaining what exactly courage or generosity amounts to in a specific situation and how exactly we might achieve it.
By developing the skill of practical wisdom, we can properly put our virtuous character traits into practice. For the Aristotelian, practical wisdom may actually be the most important virtuous disposition or character trait to develop as without the skill of practical wisdom it may be difficult to actually practice actions that are witty rather than boorish, or courageous rather than cowardly. Imagine trying to be a philosopher without an acute sense of logical reasoning; you would struggle because this seems to be a foundational good on which other philosophical skills rely. So too it may be with the virtues, practical wisdom supports our instinctive knowledge of how to respond virtuously to various feelings, emotions and situations.
If this still seems to be somewhat opaque, then we may develop our sense of practical wisdom by looking at the actions of others who we do take to be virtuous. A child, for example, will most certainly need to learn how to be virtuous by following examples of others. If we are unsure in our own ability to discern what a courageous response in a given situation is, then we may be guided by the behaviour of Socrates, Jesus, Gandhi, Mandela or King, as examples. If we learn from the wisdom and virtue of others, then just as a building apprentice learns from a master so too virtue apprentices can learn from those more skilled than they in practising virtue. Hopefully, such virtue apprentices will eventually reach a point where they can stand on their own two feet, with their personally developed sense of practical wisdom.
7. Voluntary Actions, Involuntary Actions and Moral Responsibility
Despite the focus on agents and not actions, Aristotle does have something to contribute when it comes to discussions of potential moral responsibility as associated with particular actions. We can separate actions into two obvious categories:
1. Voluntary actions
2. Involuntary actions
Very broadly, an action is voluntary when it is freely chosen and involuntary when it is not — these terms are more precisely defined next, in line with Aristotle’s ideas. These distinctions matter in ethics because a person might be held to be morally responsible for their voluntary actions but not for their involuntary actions. According to Aristotle, an action is voluntary unless it is affected by force or ignorance , as understood in the following ways.
Physical Force
Imagine that Reuben is driving his car on his way home from work. Out of the blue, his passenger grabs his hand and forces him to turn the steering wheel, sending the car into oncoming traffic. Without this physical force, Reuben would not have turned the wheel and he very much regrets the damage that is caused. According to Aristotle, Reuben’s action is involuntary because of this external physical force and so he is not morally responsible for the crash.
Psychological Force
Think of David, working at a bank when a group of thieves break in armed with guns. David is told that if he does not open the safe then he will be killed. Under this extreme psychological pressure, Aristotle would accept that David’s opening of the safe is involuntary, because David would not have opened the safe otherwise and he very much regrets doing so. On this basis, David is not morally responsible in any way for the theft.
In addition to force, ignorance of a certain type can also support an action being labelled as involuntary.
Action from Ignorance
Rhys, a talented musician, wishes to perform a surprise concert for a friend and has been practicing songs from the Barry Manilow back catalogue for weeks. However, in the days before the surprise concert his friend, unbeknown to Rhys, develops an intense and very personal dislike for Manilow. Thus, when Rhys takes to the stage and blasts out his rendition of the classic tune “Copacabana” his friend storms off in much distress. In this situation, Aristotle would accept that Rhys acted involuntarily when causing offence because he was unaware of the changed circumstances; he acted from ignorance when performing the song rather than from malice. Without this epistemic (or knowledge-related) barrier, Rhys would not have acted as he did and he very much regrets the distress caused. For these reasons, Rhys bears no moral responsibility for the upset resulting from his song choice.
Crucially, Aristotle does not allow that all action that involves ignorance can be classed as involuntary, thereby blocking associated claims of moral responsibility.
Action in Ignorance
Laurence has had too much to drink and chooses to climb a traffic light with a traffic cone on his head. Laurence’s alcohol consumption has made him ignorant, at least temporarily, of the consequences of this action in terms of social relationships, employment and police action. However, for Aristotle this would not mean that his action was involuntary because Laurence acts in ignorance rather than from ignorance due to an external epistemic (or knowledge-based) barrier. Laurence does not, therefore, escape moral responsibility as a result of his self-created ignorance.
Finally, Aristotle also identifies a third form of action — non-voluntary action — that is also related to ignorant action.
Action from Ignorance with No Regret
Return to the case of Rhys and his Manilow performance but remove any sense of regret on Rhys’ part for the distress caused. If, at the moment that the epistemic gap is bridged and Rhys learns of his friend’s newly acquired musical views, he feels no regret for his action, then Aristotle would class it as a non-voluntary rather than involuntary action. The action cannot be voluntary as Rhys acted from ignorance, but it is not obviously involuntary as, without a sense of regret, it may have been that Rhys would have performed the action even if he knew what was going to happen.
The detail above is important and your own examples will help your understanding and explanations. The summary, however, is refreshingly simple. If an action is voluntary, then it is completed free from force and ignorance and we can hold the actor morally responsible. However, if the action is involuntary then the actor is not morally responsible as they act on the basis of force or from ignorance.
8. Objection: Unclear Guidance
Consider yourself caught in the middle of a moral dilemma. Wanting to know what to do you may consult the guidance offered by Utilitarianism or Kantian Ethics and discover that various specific actions you could undertake are morally right or morally wrong. Moving to seek the advice of Aristotelian Virtue Ethics, you may find cold comfort from suggestions that you act generously, patiently and modestly whilst avoiding self-serving flattery and envy. Rather than knowing how to live in general, you may seek knowledge of what to actually do in this case. Virtue Ethics may therefore be accused of being a theory, not of helpful moral guidance, but of unhelpful and non-specific moral platitudes.
In response, the virtue ethicist may remind us that we can learn how to act from considering how truly virtuous people might respond in this situation, but this response raises its own worry — how can we identify who is virtuous, or apply their actions to a potentially novel situation? Although a defender of Virtue Ethics,
Rosalind Hursthouse
(1943–) gives a voice to this common objection, putting forward the worry directly by saying that “‘Virtue Ethics does not, because it cannot, tell us what we should do… It gives us no guidance whatsoever. Who are the virtuous agents [that we should look to for guidance]?”
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If all the virtue ethicist can offer to a person wondering how to act — perhaps wondering whether or not to report a friend to the police, or whether or not to change careers to work in the charity sector — is “look to the moral exemplars of Socrates and Gandhi and how they would act in this situation”, then we might well sympathise with the objector since very often our moral dilemmas are new situations, not merely old ones repeated. Asking “what would Jesus do”, if we deem Jesus to be a morally virtuous role model, might not seem very helpful for an MP trying to determine whether or not to vote for an increase in subsidies for renewable energy technologies at huge expense, and potential financial risk, to the tax-payer (to take a deliberately specific example).
Despite her statement of the objection, Hursthouse thinks that this is an unfair characterisation of Virtue Ethics. Hursthouse suggests that Virtue Ethics provides guidance in the form of “v-rules”. These are guiding rules of the form “do what is honest” or “avoid what is envious”.9 These rules may not be specific, but they do stand as guidance across lots of different moral situations. Whether or not you believe that this level of guidance is suitable for a normative moral theory is a judgment that you should make yourself and then defend.
9. Objection: Clashing Virtues
Related to the general objection from lack of guidance, a developed objection may question how we are supposed to cope with situations in which virtues seem to clash. Courageous behaviour may, in certain cases, mean a lack of friendliness; generosity may threaten modesty. In these situations, the suggestion to “be virtuous” may again seem to be unhelpfully vague.
To this particular objection, the Aristotelian virtue ethicist can invoke the concept of practical wisdom and suggest that the skilled and virtuous person will appropriately respond to complex moral situations. A Formula One car, for example, will be good when it has both raw speed and delicate handling and it is up to the skilled engineer to steer a path between these two virtues. So too a person with practical wisdom can steer a path between apparently clashing virtues in any given situation. Virtue ethicists have no interest in the creation of a codified moral rule book covering all situations and instead put the onus on the skill of the virtuous person when deciding how to act. Again, whether this is a strength or weakness is for you to decide and defend.
10. Objection: Circularity
An entirely different objection to Aristotelian Virtue Ethics is based on a concern regarding logical circularity. According to Aristotle, the following statements seem to be correct:
1. An act is virtuous if it is an act that a virtuous person would commit in that circumstance.
2. A person is virtuous when they act in virtuous ways.
This, however, looks to be circular reasoning. If virtuous actions are understood in terms of virtuous people, but virtuous people are understood in terms of virtuous actions, then we have unhelpfully circular reasoning.
Julia Annas
(1946–) responds to this apparent problem by arguing that there is nothing dangerously circular in this reasoning because it is simply a reflection of how we learn to develop our virtuous dispositions.
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Annas suggests the analogy of piano-playing:
1. Great piano playing is what great pianists do.
2. A pianist is great when he “does” great piano playing.
In this case, there does not seem to be any troubling circularity in reasoning. It is not the case that whatever a great pianist plays will be great, but rather that great pianists have the skills to make great music. So too it is with virtues, for virtuous people are not virtuous just because of their actual actions but because of who they are and how their actions are motivated. It is their skills and character traits that mean that, in practice, they provide a clear guide as to which actions are properly aligned with virtues. Thus, if we wish to decide whether or not an act is virtuous we can assess what a virtuous person would do in that circumstance, but this does not mean that what is virtuous is determined by the actions of a specifically virtuous individual. The issue is whether or not a person, with virtuous characteristics in the abstract, would actually carry that action out. Virtuous people are living and breathing concrete guides, helping us to understand the actions associated with abstract virtuous character dispositions.
11. Objection: Contribution to Eudaimonia
The final distinct objection to Aristotelian Virtue Ethics considered in this chapter stems from the Aristotelian claim that living virtuously will contribute to our ability to secure a
eudaimon
life. A challenge to this view may be based on the fact that certain dispositions may seem to be virtuous but may not actually seem to contribute to our flourishing or securing the good life.
As an example of this possible objection in practice, consider the following. Shelley is often described as generous to a fault and regularly dedicates large amounts of her time to helping others to solve problems at considerable cost, in terms of both time and effort, to herself. Working beyond the limits that can reasonably be expected of her, we may wish to describe Shelley as virtuous given her generous personality. However, by working herself so hard for others, we may wonder if Shelley is unduly limiting
her own
ability to flourish.
Responses to this initial statement of the objection are not hard to imagine. We may say that Shelley has either succumbed to a vice of excess and is profligate with her time rather than generous, or we may accept that she is generous rather than profligate and accept the uncomfortable conclusion and say that this virtuous character trait is helping her to flourish. This second claim may seem more plausible if we ruled out a description of Shelley wasting her time.
Still, this objection may stand up if you can envisage a situation in which someone could be properly described as rash rather than courageous or wasteful rather than generous and, because of these traits, actually be contributing to their own flourishing. You should consider your own possible cases if you seek to support this general objection.
12. Moral Good and Individual Good
For Aristotle, moral goodness and individual goodness may seem to be intimately linked. After all, a virtuous person will be charitable and friendly etc. and as a result of these characteristics and dispositions will both advance their own journey towards
eudaimonia
and make life better for others. Hedonism (which claims that pleasure is the only source of well-being — see Chapter 1), as a rival theory attempting to outline what is required for well-being, might be thought to fail because it downplays the importance of acting in accordance with reason, so hedonists do not therefore live according to their
telos
or true function.
Aristotle says of his ideally virtuous person that they will have a unified psychology — that their rational and non-rational psychologies will speak with one voice. On the contrary, the non-virtuous person will have a psychology in conflict between their rational and non-rational elements. In considering who has the better life from their own individual perspectives — the happy Hedonist or the Aristotelian virtuous person — you should again form your own reasoned judgment.
It is important to note, as we conclude this chapter, that Aristotle does not suggest that living a virtuous life is sufficient to guarantee a state of
eudaimonia
for a person. External factors such as poverty, disease or untimely death may scupper a person’s advance towards
eudaimonia
. However, for Aristotle, being virtuous is necessary for the achievement of
eudaimonia
; without the development of virtues it is impossible for a person to flourish even if they avoid poverty, disease, loneliness etc.
SUMMARY
| Aristotelian Virtue Ethics is very different in nature to the other act-centred normative moral theories considered in this book. Whether this, in itself, is a virtue or a vice is an issue for your own judgment. The lack of a codified and fixed moral rule book is something many view as a flaw, while others perceive it as the key strength of the theory. Some, meanwhile, will feel uncomfortable with Aristotle’s teleological claims, differing from those who are happy to accept that there is an objectively good life that is possible for human beings. Regardless, there is little doubt that Aristotelian Virtue Ethics offers a distinct normative moral picture and that it is a theory worthy of your reflections. |
COMMON STUDENT MISTAKES
• Understanding virtues as feelings.
• Misunderstanding the function of a human being (
eudaimonia
).
• Thinking that the Golden Mean always suggests “neutral” or “middling” actions.
• Incorrect differentiation between voluntary, involuntary and non-voluntary actions.
• Claiming that Virtue Ethics offers no guidance whatsoever in moral situations.
• Claiming that Virtue Ethics is uninterested in actions.
ISSUES TO CONSIDER
1. Who has the better life — the happy hedonist or the virtuous individual?
2. Are the virtues fixed and absolute? Or can virtues be relative to culture and time?
3. Is becoming moral a skill? Is morality based on “knowing that” or “knowing how”?
4. Can Virtue Ethics offer useful guidance?
5. Is the Golden Mean a useful way of working out virtuous characteristics?
6. Are some virtues more important than others? Why?
7. Can you think of a virtue that does not contribute to
eudaimonia
?
8. Can you think of something that contributes to
eudaimonia
that is not a virtue?
9. If there is no purpose to life, is there any point in subscribing to Aristotelian Virtue Ethics?
10. What should you do if virtues seem to clash when faced with different possible actions?
11. Who might count as virtuous role models and why?
12. Do human beings have a
telos
or proper function?
KEY TERMINOLOGY
Act-centred
Agent-centred
Dispositions
Eudaimonia
Phronesis
Virtue
Telos
Golden mean
References
Annas, Julia, Intelligent Virtue (Oxford: Oxford University Press, 2011).
Aristotle, The Nicomachean Ethics , translated by William David Ross (Oxford: Clarendon Press, 1908), freely available at http://sacred-texts.com/cla/ari/nico/index.htm
Hursthouse, Rosalind, ‘Normative Virtue Ethics’, in Ethical Theory , ed. by Russ Shafer-Landau (Oxford: Blackwell Publishing, 2007), pp. 701–09.
Panin, Ivan, Thoughts (Grafton: Ivan Panin, 1887), freely available at https://ia601405.us.archive.org/8/it...00panigoog.pdf
|
1 I. Panin,
Thoughts
, p. 92,
https://ia601405.us.archive.org/8/it...oog/thoughts00
2 Aristotle, The Nicomachean Ethics , http://sacred-texts.com/cla/ari/nico/index.htm 3 Ibid . 4 Ibid . 5 Ibid . 6 W. Durant, The Story of Philosophy , p. 76. 7 Aristotle, The Nicomachean Ethics , http://sacred-texts.com/cla/ari/nico/index.htm 8 R. Hursthouse, ‘Normative Virtue Ethics’, pp. 701–03. 9 Ibid . 10 J. Annas, Intelligent Virtue . |


1.1: Introduction
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Skills to Develop
By the end of this chapter, the student should be able to:
- Recognize and differentiate between key terms.
- Apply various types of sampling methods to data collection.
- Create and interpret frequency tables.
 If you read any newspaper, watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
Figure \(\PageIndex{1}\): We encounter statistics in our daily lives more often than we probably realize and from many different sources, like the news. (credit: David Sim)Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. Think about buying a house or managing a budget. Think about your chosen profession. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics.
Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what "good" data can be distinguished from "bad."
Contributors
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Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


7.2: Types of wetlands
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Wetlands are lands that are wet for significant periods. They are common where water and land meet. Wetlands can be large flat areas or small and steep areas. Wetlands are vibrant and unique ecosystems with many species that rely on both the land and the water for survival. Only specialized plants can grow in these conditions. Wetlands tend to have a great deal of biological diversity. Wetland ecosystems can also be fragile systems sensitive to the amounts and quality of water present within them. Learn more about wetlands further from the U.S. Environmental Protection Agency .
Types of Wetlands
There are a variety of distinct types of wetlands. Marshes are shallow wetlands around lakes, streams, or the ocean where grasses and reeds are common, but trees are not. Frogs, turtles, muskrats, and many varieties of birds are at home in marshes.
A swamp is a wetland with lush trees and vines found in a low-lying area beside slow-moving rivers. Like marshes, they are often or always inundated with water. Since the water in a swamp moves slowly, oxygen in the water is often scarce. Swamp plants and animals must be adapted for these low-oxygen conditions. Like marshes, swamps can be freshwater, saltwater, or a mixture of both.
In an estuary , salt water from the sea mixes with fresh water from a stream or river. These semi-enclosed areas are home to plants and animals that can tolerate the sharp changes in salt content that the constant motion and mixing of waters create. Estuaries contain brackish water, water that has more salt than freshwater but less than seawater. Because of the rapid changes in salt content, estuaries have many different habitats for plants, animals, and extremely high biodiversity.
Ecological Role of Wetlands
As mentioned above, wetlands are home to many varied species of organisms. Although they make up only 5 percent of the United States area, wetlands contain more than 30 percent of the plant types. Many endangered species live in wetlands, so wetlands are protected from human use. Wetlands also offer protection from storm surges from tropical storm systems like hurricanes and supply safe, hidden protection for hatchlings.
Wetlands also play a critical biological role by removing pollutants from water. For example, they can trap and use fertilizer that has washed off a farmer’s field, and therefore they prevent that fertilizer from contaminating another body of water. Since wetlands naturally purify water, preserving wetlands also help to maintain clean supplies of water.
Ponds and Lakes
Ponds and lakes are bordered by hills or low rises so that the water is blocked from flowing directly downhill. Ponds are small bodies of freshwater that usually have no outlet; ponds are often are fed by underground springs. Lakes are more substantial bodies of water. Lakes are usually freshwater, although the Great Salt Lake in Utah is just one exception. Water usually drains out of a lake through a river or a stream, and all lakes lose water to evaporation.
Large lakes have tidal systems and currents, and can even affect weather patterns. The Great Lakes in the United States contain 22 percent of the world’s fresh surface water. The largest them, Lake Superior , has a tide that rises and falls several centimeters each day. The Great Lakes are large enough to alter the Northeastern United States’ weather system by the “lake effect,” which is an increase in snow downwind of the relatively warm lakes. The Great Lakes are home to countless species of fish and wildlife.
Lakes form in various ways: in depressions carved by glaciers, in calderas, and along tectonic faults, to name a few. Subglacial lakes are even found below an ice cap. As a result of geologic history and landmasses’ arrangement, most lakes are in the Northern Hemisphere.
Limnology is the study of bodies of freshwater and the organisms that live there. The ecosystem of a lake is divided into three distinct sections:
- Surface (littoral) zone is the sloped area closest to the edge of the water.
- Open-water zone (also the photic or limnetic zone) has abundant sunlight.
- Deep-water zone (also the aphotic or profundal zone) has little or no sunlight.
There are several life zones found within a lake. In the littoral zone, sunlight promotes plant growth, which provides food and shelter to animals such as snails, insects, and fish. In the open-water zone, other plants and fish, such as bass and trout, live. The deep-water zone does not have photosynthesis since there is no sunlight. Most deep-water organisms are scavengers, such as crabs and catfish that feed on dead organisms that fall to the bottom of the lake. Fungi and bacteria aid in the decomposition in the deep zone. Though different creatures live in the oceans, ocean waters also have these same divisions based on sunlight with similar types of creatures that live in each of the zones.
Lakes are not permanent features of a landscape. Some come and go with the seasons, as water levels rise and fall. Over a longer time, lakes disappear when they fill with sediments, if the springs or streams that fill them diminish, or if their outlets grow because of erosion. When the climate of an area changes, lakes can either expand or shrink. Lakes may disappear if precipitation significantly diminishes.


7.8: Outcome- B2B Purchasing Decisions
What you’ll learn to do: explain the B2B buying process and factors influencing B2B purchasing decisions
Up to this point, our discussion about decision making has focused on individual consumers (B2C). Next we will shift attention to the decision making of businesses and other organizations when they are considering what to buy (B2B). While many of the same principles apply in business-to-business purchasing decisions, there are important differences that warrant discussion.
The specific things you’ll learn in this section include:
- Explain the B2B purchasing decision process
- Describe factors influencing B2B purchasing decisions
- Differentiate between B2C and B2B purchasing decisions
Learning Activities
The learning activities for this section include the following:
- Reading: Organizational Buying Process
- Video: Complexities of a B2B Solution Sale
- Reading: The Organizational Buying Process
- Self Check: B2B Purchasing Decisions
Contributors and Attributions
CC licensed content, Original
- Outcome: B2B Purchasing Decisions. Provided by : Lumen Learning. License : CC BY: Attribution


13.3: Evidence of Evolution
By the end of this section, you will be able to do the following:
- Explain sources of evidence for evolution
- Define homologous and vestigial structures
The evidence for evolution is compelling and extensive. Looking at every level of organization in living systems, biologists see the signature of past and present evolution. Darwin dedicated a large portion of his book, On the Origin of Species , identifying patterns in nature that were consistent with evolution and since Darwin our understanding has become clearer and broader.
Fossils
Fossils provide solid evidence that organisms from the past are not the same as those found today; fossils show a progression of evolution. Scientists determine the age of fossils and categorize them all over the world to determine when the organisms lived relative to each other. The resulting fossil record tells the story of the past, and shows the evolution of form over millions of years (Figure \(\PageIndex{1}\)). For example, highly detailed fossil records have been recovered for sequences of species in the evolution of whales and modern horses. The fossil record of horses in North America is especially rich and many contain transition fossils: those showing intermediate anatomy between earlier and later forms. The fossil record extends back to a dog-like ancestor some 55 million years ago that gave rise to the first horse-like species 55 to 42 million years ago in the genus Eohippus . The series of fossils tracks the change in anatomy resulting from a gradual drying trend that changed the landscape from a forested one to a prairie. Successive fossils show the evolution of teeth shapes and foot and leg anatomy to a grazing habit, with adaptations for escaping predators, for example in species of Mesohippus found from 40 to 30 million years ago. Later species showed gains in size, such as those of Hipparion , which existed from about 23 to 2 million years ago. The fossil record shows several adaptive radiations in the horse lineage, which is now much reduced to only one genus, Equus , with several species.
Anatomy and Embryology
Another type of evidence for evolution is the presence of structures in organisms that share the same basic form. For example, the bones in the appendages of a human, dog, bird, and whale all share the same overall construction (Figure \(\PageIndex{2}\)). That similarity results from their origin in the appendages of a common ancestor. Over time, evolution led to changes in the shapes and sizes of these bones in different species, but they have maintained the same overall layout, evidence of descent from a common ancestor. Scientists call these synonymous parts homologous structures. Some structures exist in organisms that have no apparent function at all, and appear to be residual parts from a past ancestor. For example, some snakes have pelvic bones despite having no legs because they descended from reptiles that did have legs. These unused structures without function are called vestigial structures. Other examples of vestigial structures are wings on flightless birds (which may have other functions), leaves on some cacti, traces of pelvic bones in whales, and the sightless eyes of cave animals.
Another evidence of evolution is the convergence of form in organisms that share similar environments. For example, species of unrelated animals, such as the arctic fox and ptarmigan (a bird), living in the arctic region have temporary white coverings during winter to blend with the snow and ice (Figure \(\PageIndex{3}\)). The similarity occurs not because of common ancestry, indeed one covering is of fur and the other of feathers, but because of similar selection pressures—the benefits of not being seen by predators.
Embryology, the study of the development of the anatomy of an organism to its adult form also provides evidence of relatedness between now widely divergent groups of organisms. Structures that are absent in some groups often appear in their embryonic forms and disappear by the time the adult or juvenile form is reached. For example, all vertebrate embryos, including humans, exhibit gill slits at some point in their early development. These disappear in the adults of terrestrial groups, but are maintained in adult forms of aquatic groups such as fish and some amphibians. Great ape embryos, including humans, have a tail structure during their development that is lost by the time of birth. The reason embryos of unrelated species are often similar is that mutational changes that affect the organism during embryonic development can cause amplified differences in the adult, even while the embryonic similarities are preserved.
Biogeography
The geographic distribution of organisms on the planet follows patterns that are best explained by evolution in conjunction with the movement of tectonic plates over geological time. Broad groups that evolved before the breakup of the supercontinent Pangaea (about 200 million years ago) are distributed worldwide. Groups that evolved since the breakup appear uniquely in regions of the planet, for example the unique flora and fauna of northern continents that formed from the supercontinent Laurasia and of the southern continents that formed from the supercontinent Gondwana. The presence of Proteaceae in Australia, southern Africa, and South America is best explained by the plant family’s presence there prior to the southern supercontinent Gondwana breaking up (Figure \(\PageIndex{4}\)).
The great diversification of the marsupials in Australia and the absence of other mammals reflects that island continent’s long isolation. Australia has an abundance of endemic species—species found nowhere else—which is typical of islands whose isolation by expanses of water prevents migration of species to other regions. Over time, these species diverge evolutionarily into new species that look very different from their ancestors that may exist on the mainland. The marsupials of Australia, the finches on the Galápagos, and many species on the Hawaiian Islands are all found nowhere else but on their island, yet display distant relationships to ancestral species on mainlands.
Molecular Biology
Like anatomical structures, the structures of the molecules of life reflect descent with modification. Evidence of a common ancestor for all of life is reflected in the universality of DNA as the genetic material and of the near universality of the genetic code and the machinery of DNA replication and expression. Fundamental divisions in life between the three domains are reflected in major structural differences in otherwise conservative structures such as the components of ribosomes and the structures of membranes. In general, the relatedness of groups of organisms is reflected in the similarity of their DNA sequences—exactly the pattern that would be expected from descent and diversification from a common ancestor.
DNA sequences have also shed light on some of the mechanisms of evolution. For example, it is clear that the evolution of new functions for proteins commonly occurs after gene duplication events. These duplications are a kind of mutation in which an entire gene is added as an extra copy (or many copies) in the genome. These duplications allow the free modification of one copy by mutation, selection, and drift, while the second copy continues to produce a functional protein. This allows the original function for the protein to be kept, while evolutionary forces tweak the copy until it functions in a new way.
Contributors and Attributions
Remixed and/or curated from the following works:
- Fowler, S., Roush, R., & Wise, J. (2013). 11.3 Evidence of Evolution . In Concepts of Biology . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/concepts-biology/pages/1-introduction ).


4.6: Writing for Success- Narration
This section will help you determine the purpose and structure of narration in writing.
The Purpose of Narrative Writing
Narration means the art of storytelling, and the purpose of narrative writing is to tell stories. Any time you tell a story to a friend or family member about an event or incident in your day, you engage in a form of narration. In addition, a narrative can be factual or fictional. A factual story is one that is based on, and tries to be faithful to, actual events as they unfolded in real life. A fictional story is a made-up, or imagined, story; the writer of a fictional story can create characters and events as he or she sees fit.
The big distinction between factual and fictional narratives is based on a writer’s purpose. The writers of factual stories try to recount events as they actually happened, but writers of fictional stories can depart from real people and events because the writers’ intents are not to retell a real-life event. Biographies and memoirs are examples of factual stories, whereas novels and short stories are examples of fictional stories.
Know Your Purpose
Because the line between fact and fiction can often blur, it is helpful to understand what your purpose is from the beginning. Is it important that you recount history, either your own or someone else’s? Or does your interest lie in reshaping the world in your own image—either how you would like to see it or how you imagine it could be? Your answers will go a long way in shaping the stories you tell.
Ultimately, whether the story is fact or fiction, narrative writing tries to relay a series of events in an emotionally engaging way. You want your audience to be moved by your story, which could mean through laughter, sympathy, fear, anger, and so on. The more clearly you tell your story, the more emotionally engaged your audience is likely to be.
The Structure of a Narrative Essay
Major narrative events are most often conveyed in chronological order, the order in which events unfold from first to last. Stories typically have a beginning, a middle, and an end, and these events are typically organized by time. Certain transitional words and phrases aid in keeping the reader oriented in the sequencing of a story. Some of these phrases are listed here:
| after/afterward | as soon as | at last | before |
| currently | during | eventually | meanwhile |
| next | now | since | soon |
| finally | later | still | then |
| until | when/whenever | while | first, second, third |
Other basic components of a narrative are:
- Plot – The events as they unfold in sequence.
- Characters – The people who inhabit the story and move it forward. Typically, there are minor characters and main characters. The minor characters generally play supporting roles to the main character, also known as the protagonist.
- Conflict – The primary problem or obstacle that unfolds in the plot that the protagonist must solve or overcome by the end of the narrative. The way in which the protagonist resolves the conflict of the plot results in the theme of the narrative.
- Theme – The ultimate message the narrative is trying to express; it can be either explicit or implicit.
Writing a Narrative Essay
When writing a narrative essay, start by asking yourself if you want to write a factual or fictional story. Then freewrite, brainstorm, or mindmap about topics that are of general interest to you. For more information about pre-writing, review the materials in “My Writing Process – Prewriting and Draft.”
Once you have a general idea of what you will be writing about, you should sketch out the major events of the story that will compose your plot. Typically, these events will be revealed chronologically and climax at a central conflict that must be resolved by the end of the story. The use of strong details is crucial as you describe the events and characters in your narrative. You want the reader to emotionally engage with the world that you create in writing.
Keep the Senses in Mind
To create strong details, keep the human senses in mind. You want your reader to be immersed in the world that you create, so focus on details related to sight, sound, smell, taste, and touch as you describe people, places, and events in your narrative.
As always, it is important to start with a strong introduction to hook your reader into wanting to read more. Try opening the essay with an event that is interesting to introduce the story and get it going. Finally, your conclusion should help resolve the central conflict of the story and impress upon your reader the ultimate theme of the piece.
 You may have had a horrible experience at a restaurant the night before, or you may have had some good news you are ready to share. In each one of these experiences there’s a story, and when you begin to share a personal experience, you often communicate in a narrative mode.
Although narratives can vary widely, most share several common features. Generally, storytellers establish:
- Characters , the person/people (sometimes they are animals) the story is about, which may include the storyteller
- Conflict , or struggle in the story, that builds their audience’s interest
- Details , or descriptions, that appeal to the senses of sight, sound, smell, touch, and taste
- A sequence of events in a plot , or order of what happens in the story, that keeps the audience engaged as the story unfolds
- Reflection of events around a theme , or unifying idea, for telling the story
Narratives of Love and War
Consider two narratives that couldn’t be more different—a tale of love and a story of war: John Hodgman’s sweet, geeky tale of falling in love and Emmanuel Jal’s story of being a child soldier and learning to forgive his enemies. Review these videos below then engage in a discussion following the directions as listed.
John Hodgman: A Brief Digression on Matters of Lost Time
Emmanuel Jal: The Music of a War Child
Narrative Essay Example
Read the following example of a narrative essay. Note how it reflects the basic components and common features of narratives, as discussed above.
My College Education
By Scott McLean, in Writing for Success
The first class I went to in college was philosophy, and it changed my life forever. Our first assignment was to write a short response paper to the Albert Camus essay “The Myth of Sisyphus.” I was extremely nervous about the assignment as well as college. However, through all the confusion in philosophy class, many of my questions about life were answered.
I entered college intending to earn a degree in engineering. I always liked the way mathematics had right and wrong answers. I understood the logic and was very good at it. So when I received my first philosophy assignment that asked me to write my interpretation of the Camus essay, I was instantly confused. What is the right way to do this assignment, I wondered? I was nervous about writing an incorrect interpretation and did not want to get my first assignment wrong. Even more troubling was that the professor refused to give us any guidelines on what he was looking for; he gave us total freedom. He simply said, “I want to see what you come up with.”
Full of anxiety, I first set out to read Camus’s essay several times to make sure I really knew what was it was about. I did my best to take careful notes. Yet even after I took all these notes and knew the essay inside and out, I still did not know the right answer. What was my interpretation? I could think of a million different ways to interpret the essay, but which one was my professor looking for? In math class, I was used to examples and explanations of solutions. This assignment gave me nothing; I was completely on my own to come up with my individual interpretation.
Next, when I sat down to write, the words just did not come to me. My notes and ideas were all present, but the words were lost. I decided to try every prewriting strategy I could find. I brainstormed, made idea maps, and even wrote an outline. Eventually, after a lot of stress, my ideas became more organized and the words fell on the page. I had my interpretation of “The Myth of Sisyphus,” and I had my main reasons for interpreting the essay. I remember being unsure of myself, wondering if what I was saying made sense, or if I was even on the right track. Through all the uncertainty, I continued writing the best I could. I finished the conclusion paragraph, had my spouse proofread it for errors, and turned it in the next day simply hoping for the best.
Then, a week or two later, came judgment day. The professor gave our papers back to us with grades and comments. I remember feeling simultaneously afraid and eager to get the paper back in my hands. It turned out, however, that I had nothing to worry about. The professor gave me an A on the paper, and his notes suggested that I wrote an effective essay overall. He wrote that my reading of the essay was very original and that my thoughts were well organized. My relief and newfound confidence upon reading his comments could not be overstated.
What I learned through this process extended well beyond how to write a college paper. I learned to be open to new challenges. I never expected to enjoy a philosophy class and always expected to be a math and science person. This class and assignment, however, gave me the selfconfidence, critical-thinking skills, and courage to try a new career path. I left engineering and went on to study law and eventually became a lawyer. More important, that class and paper helped me understand education differently. Instead of seeing college as a direct stepping stone to a career, I learned to see college as a place to first learn and then seek a career or enhance an existing career. By giving me the space to express my own interpretation and to argue for my own values, my philosophy class taught me the importance of education for education’s sake. That realization continues to pay dividends every day.
Key Takeaways
- Narration is the art of storytelling.
- Narratives can be either factual or fictional. In either case, narratives should emotionally engage the reader.
- Most narratives are composed of major events sequenced in chronological order.
- Time transition words and phrases are used to orient the reader in the sequence of a narrative.
- The four basic components to all narratives are plot, character, conflict, and theme.
- The use of sensory details is crucial to emotionally engaging the reader.
- A strong introduction is important to hook the reader. A strong conclusion should add resolution to the conflict and evoke the narrative’s theme.


7.5E: Exercises
Solve Rational Equations
In the following exercises, solve each rational equation.
1. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)
- Answer
-
\(a=10\)
2. \(\dfrac{6}{3}-\dfrac{2}{d}=\dfrac{4}{9}\)
3. \(\dfrac{4}{5}+\dfrac{1}{4}=\dfrac{2}{v}\)
- Answer
-
\(v=\dfrac{40}{21}\)
4. \(\dfrac{3}{8}+\dfrac{2}{y}=\dfrac{1}{4}\)
5. \(1-\dfrac{2}{m}=\dfrac{8}{m^{2}}\)
- Answer
-
\(m=-2,\; m=4\)
6. \(1+\dfrac{4}{n}=\dfrac{21}{n^{2}}\)
7. \(1+\dfrac{9}{p}=\dfrac{-20}{p^{2}}\)
- Answer
-
\(p=-5, \; p=-4\)
8. \(1-\dfrac{7}{q}=\dfrac{-6}{q^{2}}\)
9. \(\dfrac{5}{3 v-2}=\dfrac{7}{4 v}\)
- Answer
-
\(v=14\)
10. \(\dfrac{8}{2 w+1}=\dfrac{3}{w}\)
11. \(\dfrac{3}{x+4}+\dfrac{7}{x-4}=\dfrac{8}{x^{2}-16}\)
- Answer
-
\(x=-\dfrac{4}{5}\)
12. \(\dfrac{5}{y-9}+\dfrac{1}{y+9}=\dfrac{18}{y^{2}-81}\)
13. \(\dfrac{8}{z-10}-\dfrac{7}{z+10}=\dfrac{5}{z^{2}-100}\)
- Answer
-
\(z=-145\)
14. \(\dfrac{9}{a+11}-\dfrac{6}{a-11}=\dfrac{6}{a^{2}-121}\)
15. \(\dfrac{-10}{q-2}-\dfrac{7}{q+4}=1\)
- Answer
-
\(q=-18, \; q=-1\)
16. \(\dfrac{2}{s+7}-\dfrac{3}{s-3}=1\)
17. \(\dfrac{v-10}{v^{2}-5 v+4}=\dfrac{3}{v-1}-\dfrac{6}{v-4}\)
- Answer
-
no solution
18. \(\dfrac{w+8}{w^{2}-11 w+28}=\dfrac{5}{w-7}+\dfrac{2}{w-4}\)
19. \(\dfrac{x-10}{x^{2}+8 x+12}=\dfrac{3}{x+2}+\dfrac{4}{x+6}\)
- Answer
-
no solution
20. \(\dfrac{y-5}{y^{2}-4 y-5}=\dfrac{1}{y+1}+\dfrac{1}{y-5}\)
21. \(\dfrac{b+3}{3 b}+\dfrac{b}{24}=\dfrac{1}{b}\)
- Answer
-
\(b=-8\)
22. \(\dfrac{c+3}{12 c}+\dfrac{c}{36}=\dfrac{1}{4 c}\)
23. \(\dfrac{d}{d+3}=\dfrac{18}{d^{2}-9}+4\)
- Answer
-
\(d=2\)
24. \(\dfrac{m}{m+5}=\dfrac{50}{m^{2}-25}+6\)
25. \(\dfrac{n}{n+2}-3=\dfrac{8}{n^{2}-4}\)
- Answer
-
\(m=1\)
26. \(\dfrac{p}{p+7}-8=\dfrac{98}{p^{2}-49}\)
27. \(\dfrac{q}{3 q-9}-\dfrac{3}{4 q+12}=\dfrac{7 q^{2}+6 q+63}{24 q^{2}-216}\)
- Answer
-
no solution
28. \(\dfrac{r}{3 r-15}-\dfrac{1}{4 r+20}=\dfrac{3 r^{2}+17 r+40}{12 r^{2}-300}\)
29. \(\dfrac{s}{2 s+6}-\dfrac{2}{5 s+5}=\dfrac{5 s^{2}-3 s-7}{10 s^{2}+40 s+30}\)
- Answer
-
\(s=\dfrac{5}{4}\)
30. \(\dfrac{t}{6 t-12}-\dfrac{5}{2 t+10}=\dfrac{t^{2}-23 t+70}{12 t^{2}+36 t-120}\)
31. \(\dfrac{2}{x^{2}+2 x-8}-\dfrac{1}{x^{2}+9 x+20}=\dfrac{4}{x^{2}+3 x-10}\)
- Answer
-
\(x=-\dfrac{4}{3}\)
32. \(\dfrac{5}{x^{2}+4 x+3}+\dfrac{2}{x^{2}+x-6}=\dfrac{3}{x^{2}-x-2}\)
33. \(\dfrac{3}{x^{2}-5 x-6}+\dfrac{3}{x^{2}-7 x+6}=\dfrac{6}{x^{2}-1}\)
- Answer
-
no solution
34. \(\dfrac{2}{x^{2}+2 x-3}+\dfrac{3}{x^{2}+4 x+3}=\dfrac{6}{x^{2}-1}\)
Solve Rational Equations that Involve Functions
35. For rational function, \(f(x)=\dfrac{x-2}{x^{2}+6 x+8}\):
- Find the domain of the function
- Solve \(f(x)=5\)
- Find the points on the graph at this function value
- Answer
-
- The domain is all real numbers except \(x \neq-2\) and \(x \neq-4\)
- \(x=-3, x=-\dfrac{14}{5}\)
- \((-3,5),\left(-\dfrac{14}{5}, 5\right)\)
36. For rational function, \(f(x)=\dfrac{x+1}{x^{2}-2 x-3}\):
- Find the domain of the function
- Solve \(f(x)=1\)
- Find the points on the graph at this function value
37. For rational function, \(f(x)=\dfrac{2-x}{x^{2}-7 x+10}\):
- Find the domain of the function
- Solve \(f(x)=2\)
- Find the points on the graph at this function value
- Answer
-
- The domain is all real numbers except \(x \neq 2\) and \(x \neq 5\)
- \(x=\dfrac{9}{2}\)
- \(\left(\dfrac{9}{2}, 2\right)\)
38. For rational function, \(f(x)=\dfrac{5-x}{x^{2}+5 x+6}\):
- Find the domain of the function
- Solve \(f(x)=3\)
- Find the points on the graph at this function value
Solve a Rational Equation for a Specific Variable
In the following exercises, solve:
39. \(\dfrac{c}{r}=2 \pi \text { for } r\)
- Answer
-
\(r=\dfrac{C}{2 \pi}\)
40. \(\dfrac{I}{r}=P \text { for } r\)
41. \(\dfrac{v+3}{w-1}=\dfrac{1}{2} \text { for } w\)
- Answer
-
\(w=2 v+7\)
42. \(\dfrac{x+5}{2-y}=\dfrac{4}{3} \text { for } y\)
43. \(a=\dfrac{b+3}{c-2} \text { for } c\)
- Answer
-
\(c=\dfrac{b+3+2 a}{a}\)
44. \(m=\dfrac{n}{2-n} \text { for } n\)
45. \(\dfrac{1}{p}+\dfrac{2}{q}=4 \text { for } p\)
- Answer
-
\(p=\dfrac{q}{4 q-2}\)
46. \(\dfrac{3}{s}+\dfrac{1}{t}=2 \text { for } s\)
47. \(\dfrac{2}{v}+\dfrac{1}{5}=\dfrac{3}{w} \text { for } w\)
- Answer
-
\(w=\dfrac{15 v}{10+v}\)
48. \(\dfrac{6}{x}+\dfrac{2}{3}=\dfrac{1}{y} \text { for } y\)
49. \(\dfrac{m+3}{n-2}=\dfrac{4}{5} \text { for } n\)
- Answer
-
\(n=\dfrac{5 m+23}{4}\)
50. \(r=\dfrac{s}{3-t} \text { for } t\)
51. \(\dfrac{E}{c}=m^{2} \text { for } c\)
- Answer
-
\(c=\dfrac{E}{m^{2}}\)
52. \(\dfrac{R}{T}=W \text { for } T\)
53. \(\dfrac{3}{x}-\dfrac{5}{y}=\dfrac{1}{4} \text { for } y\)
- Answer
-
\(y=\dfrac{20 x}{12-x}\)
54. \(c=\dfrac{2}{a}+\dfrac{b}{5} \text { for } a\)
Writing Exercises
55. Your class mate is having trouble in this section. Write down the steps you would use to explain how to solve a rational equation.
- Answer
-
Answers will vary.
56. Alek thinks the equation \(\dfrac{y}{y+6}=\dfrac{72}{y^{2}-36}+4\) has two solutions, \(y=-6\) and \(y=4\). Explain why Alek is wrong.


20.16: Discussion- Grocery Shopping
Purpose
You will research and compare the nutritional characteristics and affordability of foods from various sources. You will discuss this information with your classmates.
Directions
Go to discussion board to complete this assignment. You will need to complete an independent experiment and then answer these questions based on your findings:
- Pretend I gave you ten dollars to purchase food (in this pretend world there is no such thing as taxes).
- Go to a fast food restaurant, look at the menu, and see how much you can purchase (I am not encouraging you to buy anything and I hope you will not).
- Your items should include something to eat and something to drink. Make a list of everything you could buy.
- Then, go to a grocery store and see how much you can purchase for the same ten dollars (again, I am not encouraging you to buy anything and you do not need to buy anything to complete this assignment). Again, make a list of everything you could buy.
- For comparative purposes, the end meals should be as similar as possible. To make your comparison easier to see (for you and for your classmates), it is best to make your lists either side by side or one right after the other (a chart is a very good idea) before you begin your discussion.
- Your discussion and comparison should include the approximate number of meals/servings you could make from your purchases, and should also address any differences in calories between the two.
- Also suggest a similar but healthier alternative to these meals.
- Submit your original response.
- Respond to 2 of your classmates’ discussions. No attachments, please!
Note: You will not be able to see your classmates’ discussions until you post your own.
Grading
This assignment is worth 10 points maximum. Your grade will be assessed based on the Grocery Shopping Grading Rubric:
|
Criteria |
Novice |
Competent |
Proficient |
|
Original entry |
0 points |
3.5 points
Up to 3.5 points if submitted late or missing parts. |
7 points
Thorough entry submitted by the deadline. The entry must include food/drink items from both locations (fast food restaurant and grocery store) and the comparison addressing all discussion points listed in the assignment instructions. |
|
Response to two classmates |
0 points |
1 Point
Up to 1 point if late or
|
2 Points Well-constructed responses to two classmates addressing the classmate original posting and submitted by the deadline. |
|
Grammar and organization |
0 points | 0 points |
1 Point |
- Lifetime Fitness and Wellness. Provided by : Extended Learning Institute of Northern Virginia Community College. Located at : https://eli.nvcc.edu/ . License : CC BY: Attribution


7.5: Full Hypothesis Test Examples
Tests on Means
Example \(\PageIndex{1}\)
Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle.
His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims . For the 15 swims, Jeffrey's mean time was 16 seconds , with a standard deviation of 0.8 seconds . Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using test statistics and \(p\)-values with a preset \(\alpha = 0.05\).
- Answer
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Set up the Hypothesis Test:
Since the problem is about a mean, this is a test of a single population mean .
Set the null and alternative hypothesis:
In this case there is an implied challenge or claim. This is that the goggles will reduce the swimming time. The effect of this is to set the hypothesis as a one-tailed test. The claim will always be in the alternative hypothesis because the burden of proof always lies with the alternative. Remember that the status quo must be defeated with a high degree of confidence, in this case 95% confidence. The null and alternative hypotheses are thus:
\(H_0: \mu \geq 16.43\) \(H_a: \mu < 16.43\)
For Jeffrey to swim faster, his time should be less than 16.43 seconds. The "<" tells you this is left-tailed.
Determine the distribution needed:
Random variable: \(\overline x\) = the mean time to swim the 25-yard freestyle.
Distribution for the test statistic:
The sample size is less than 30 and we do not know the population standard deviation so this is a t -test. The proper formula is: \(t_{obs}=\frac{\overline{x}-\mu_{0}}{s / \sqrt{n}}\)
\(\mu_ 0 = 16.43\) comes from \(H_0\) and not the data. \(\overline x = 16\), \(s = 0.8\), and \(n = 15\).
Our step 2, setting the level of confidence, has already been determined by the problem, \(\alpha\) of .05 corresponds to a 95% confidence level. It is worth thinking about the meaning of this choice. The Type I error is to conclude that Jeffrey swims the 25-yard freestyle, on average, in less than 16.43 seconds when, in fact, he actually swims the 25-yard freestyle, on average, in 16.43 seconds or more. (Reject the null hypothesis when the null hypothesis is true.) For this case the only concern with a Type I error would seem to be that Jeffrey’s dad may fail to bet on his son’s victory because he does not have appropriate confidence in the effect of the goggles.
To find the critical value we need to select the appropriate test statistic. We have concluded that this is a t -test on the basis of the sample size and that we are interested in a population mean. We can now draw the graph of the t -distribution and mark the critical value. For this problem the degrees of freedom are n-1, or 14. Looking up 14 degrees of freedom at the 0.05 column of the t -table we find 1.761. This is the critical value and we can put this on our graph.
Step 3 is the calculation of the test statistic using the formula we have selected. We find that the observed test statistic is -2.08, meaning that the sample mean is 2.08 standard errors below the hypothesized mean of 16.43.
\[t_{obs}=\frac{\overline{x}-\mu_{0}}{s / \sqrt{n}}=\frac{16-16.43}{.8 / \sqrt{15}}=-2.08\nonumber\]
Step 4 has us compare the test statistic and the critical value and mark these on the graph. We see that the test statistic is in the tail and thus we move to step 4 and reach a conclusion. The probability that an average time of 16 minutes could come from a distribution with a population mean of 16.43 minutes is too unlikely to have occurred under the null hypothesis. We reject the null.
Step 5 has us state our conclusions first formally and then less formally. A formal conclusion would be stated as: “With a 95% level of confidence we reject the null hypothesis that the swimming time with goggles comes from a distribution with a population mean time of 16.43 minutes.” Less formally, “With 95% confidence, we believe that the goggles improved swimming speed".
If we wished to use the \(p\)-value system of reaching a conclusion we would calculate the statistic and take the additional step to find the probability of being 2.08 standard errors from the mean on a t -distribution. The \(p\)-value interval is (.025, .05), that we get by looking up the one-tailed probabilities associated with the closest t -scores (1.761 and 2.145) to the observed test statistic (-2.08) in the relevant df row of 14 in the t -table. Comparing this interval to the significance level of .05 we see that we reject the null. The \(p\)-value has been put on the graph as the shaded area beyond -2.08 and it shows that it is smaller than the hatched area which is the \(\alpha\) level of 0.05. Both methods reach the same conclusion that we reject the null hypothesis.
Exercise \(\PageIndex{1}\)
The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset \(\alpha = 0.05\). Assume the throw distances for footballs are normal.
First, determine what type of test this is, set up the hypothesis test, find the \(p\)-value, sketch the graph, and state your conclusion.
Example \(\PageIndex{2}\)
Jane has just begun her new job as on the sales force of a very competitive company. In a sample of 16 sales calls it was found that she closed the contract for an average value of 108 dollars with a standard deviation of 12 dollars. Company policy requires that new members of the sales force must exceed an average of $100 per contract during the trial employment period. Can we conclude that Jane has met this requirement at the significance level of 5%?
- Answer
-
-
\(H_0: \mu \leq 100\)
\(H_a: \mu > 100\)
The null and alternative hypothesis are for the parameter \(\mu\) because the number of dollars of the contracts is a continuous random variable. Also, this is a one-tailed test because the company has only an interested if the number of dollars per contact is below a particular number not "too high" a number. This can be thought of as making a claim that the requirement is being met and thus the claim is in the alternative hypothesis. - Test statistic: \(t_{obs}=\frac{\overline{x}-\mu_{0}}{\frac{s}{\sqrt{n}}}=\frac{108-100}{\left(\frac{12}{\sqrt{16}}\right)}=2.67\)
- Critical value: \(t_\alpha=1.753\) with \(n-1\) degrees of freedom = 15
The test statistic is a Student's t because the sample size is below 100; therefore, we cannot use the normal distribution. Comparing the observed value of the test statistic and the critical value of t at a 5% significance level, we see that the observed value is in the tail of the distribution. Thus, we conclude that 108 dollars per contract is significantly larger than the hypothesized value of 100 and thus we must reject the null hypothesis. There is evidence that Jane's performance meets company standards.
-
\(H_0: \mu \leq 100\)
Exercise \(\PageIndex{2}\)
It is believed that a stock price for a particular company will grow at a rate of $5 per week with a standard deviation of $1. An investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. Perform a hypothesis test using a 5% level of significance. State the null and alternative hypotheses, state your conclusion, and identify the Type I and Type II errors.
Example \(\PageIndex{3}\)
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses salad dressings is working properly when 8 ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles is 7.91 ounces with a variance of 0.03 ounces squared, \(s^2\). Is there evidence that the machine should be stopped and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of confidence in the analysis should be 99%.
Again we will follow the steps in our analysis of this problem.
- Answer
-
STEP 1 : Set the null and alternative hypothesis.
The random variable is the quantity of fluid placed in the bottles. This is a continuous random variable and the parameter we are interested in is the mean. Our hypothesis therefore is about the mean. In this case we are concerned that the machine is not filling properly. From what we are told it does not matter if the machine is over-filling or under-filling, both seem to be an equally bad error. This tells us that this is a two-tailed test: if the machine is malfunctioning it will be shutdown regardless if it is from over-filling or under-filling. The null and alternative hypotheses are thus:
\[H_0:\mu=8\nonumber\]
\[Ha:\mu \neq 8\nonumber\]
STEP 2 : Decide the level of significance and draw the graph showing the critical value.
This problem has already set the level of confidence at 99%. The decision seems an appropriate one and shows the thought process when setting the significance level. Management wants to be very certain, as certain as probability will allow, that they are not shutting down a machine that is not in need of repair. To draw the distribution and the critical value, we need to know which distribution to use. Because the sample size is under 100, the appropriate distribution is the t -distribution and the relevant critical value is 2.750 from the t -table at 0.005 column and 30 degrees of freedom (closest available row to our actual 34 df here). We need to draw the graph and mark these points.
STEP 3 : Calculate sample parameters and the test statistic.
The sample parameters are provided, the sample mean is 7.91 and the sample variance is .03 and the sample size is 35. We need to note that the sample variance was provided, not the sample standard deviation, which is what we need for the formula. Remembering that the standard deviation is simply the square root of the variance, we therefore know the sample standard deviation, \(s\), is 0.173. With this information we can calculate the test statistic as -3.07, and mark it on the graph.
\[t_{obs}=\frac{\overline{x}-\mu_{0}}{s / \sqrt{n}}=\frac{7.91-8}{\cdot 173 / \sqrt{35}}=-3.07\nonumber\]
STEP 4 : Compare test statistic and the critical values.
Now we compare the test statistic and the critical value by placing the test statistic on the graph. The test statistic is in the tail, decidedly greater than the critical value of 2.750. We note that even the very small difference between the hypothesized value and the sample value is still a large number of standard errors. The sample mean is only 0.08 ounces different from the required level of 8 ounces, but it is 3+ standard errors away from the required 8 ounces, and thus we reject the null hypothesis.
STEP 5 : Reach a conclusion.
Three standard errors of a test statistic will guarantee that the test will fail. The probability that anything is beyond three standard errors of a hypothesized null value - given a large enough sample size - is close to zero. Looking at the closest t -scores in df =30 row in the t -table, we get the \(p\)-value interval of (.01, .002) after doubling the one-tailed probabilities of .005 and .001. Our formal conclusion would be “At a 99% level of confidence, we reject the null hypothesis that the sample mean came from a distribution with a mean of 8 ounces”. Or less formally, and getting to the point, “At a 99% level of confidence, we conclude that the machine is under-filling the bottles and is in need of repair”.
Hypothesis Test for Proportions
Just as there were confidence intervals for proportions, or more formally, the population parameter \(P\), there is the ability to test hypotheses concerning \(P\).
The estimated value (point estimate) for \(P\) is \(P^{\prime}\) where \(P^{\prime} = x/n\), \(x\) is the number of observations in the category of interest in the sample and \(n\) is the sample size.
When you perform a hypothesis test of a population proportion \(P\), you take a random sample from the population. To ensure normality of the distribution, sampling must be random and the total sample size must be greater than 100. There is no distribution that can correct for this small sample bias and thus if these conditions are not met we simply cannot test the hypothesis with the data available at that time. We met this condition when we were first estimating confidence intervals for \(P\).
Again, we begin with the modified standardizing formula:
\[z=\frac{P^{\prime}-P}{\sqrt{\frac{P(1-P)}{n}}}\nonumber\]
Substituting \(P_0\), the hypothesized value of \(P\), we have:
\[z_{obs}=\frac{P^{\prime}-P_{0}}{\sqrt{\frac{P_{0} (1-P_{0})}{n}}}\nonumber\]
This is the test statistic for testing hypothesized values of \(P\), where the null and alternative hypotheses take one of the following forms:
| Two-tailed test | One-tailed test | One-tailed test |
|---|---|---|
| \(H_0: P = P_0\) | \(H_0: P \leq P_0\) | \(H_0: P \geq P_0\) |
| \(H_a: P \neq P_0\) | \(H_a: P > P_0\) | \(H_a: P < P_0\) |
Table \(\PageIndex{1}\)
The decision rule stated above applies here also: if the calculated value of \(z_{obs}\) shows that the sample proportion is "too many" standard errors from the hypothesized proportion, the null hypothesis is rejected. The decision as to what is "too many" is pre-determined by the analyst depending on the level of significance required in the test.
Example \(\PageIndex{4}\)
The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 50% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is different from 50% . They sample 101 first-time borrowers and find 54 of these loans are smaller that the other borrowers. For the hypothesis test, they choose a 5% level of significance.
- Answer
-
STEP 1 : Set the null and alternative hypothesis.
\(H_0: P = 0.50\) \(H_a: P \neq 0.50\)
The words "is different from" tell you this is a two-tailed test. The Type I and Type II errors are as follows: The Type I error is to conclude that the proportion of borrowers is different from 50% when, in fact, the proportion is actually 50%. (Reject the null hypothesis when the null hypothesis is true). The Type II error is there is not enough evidence to conclude that the proportion of first time borrowers differs from 50% when, in fact, the proportion does differ from 50%. (You fail to reject the null hypothesis when the null hypothesis is false.)
STEP 2 : Decide the level of significance and draw the graph showing the critical value
The level of confidence has been set by the problem at 95%. Because this is two-tailed test one-half of the \(\alpha\) value will be in the upper tail and one-half in the lower tail as shown on the graph. The critical value for the normal distribution at the 95% level of confidence is 1.96. This can easily be found on the Student’s t -table at the very bottom at infinite degrees of freedom remembering that at infinity the t -distribution is the normal distribution. Of course, the value can also be found on the standard normal table but you have go looking for the tail probability, \(\alpha\)/2, inside the body of the table and then read out to the sides and top for the number of standard errors.
STEP 3 : Calculate the sample parameters and critical value of the test statistic.
The test statistic is a normal distribution, \(z\), for testing proportions and is:
\[z=\frac{P^{\prime}-P_{0}}{\sqrt{\frac{P_{0} (1-P_{0})}{n}}}=\frac{.53-.50}{\sqrt{\frac{.5(.5)}{101}}}=0.60\nonumber\]
For this case, the sample of 101 found 54 first-time borrowers were different from other borrowers. The sample proportion, \(P^{\prime} = 54/101= 0.53\) The test question, therefore, is : “Is 0.53 significantly different from 0.50?” Putting these values into the formula for the test statistic we find that 0.53 is only 0.60 standard errors away from 0.50. This is barely off of the mean of the standard normal distribution of zero. There is virtually no difference from the sample proportion and the hypothesized proportion in terms of standard errors.
STEP 4 : Compare the test statistic and the critical value.
The observed value is well within the critical values of \(\pm 1.96\) standard errors and thus we cannot reject the null hypothesis. To reject the null hypothesis we need significant evidence of difference between the hypothesized value and the sample value. In this case the sample value is very nearly the same as the hypothesized value measured in terms of standard errors.
STEP 5 : Reach a conclusion.
The formal conclusion would be “At a 95% level of confidence we cannot reject the null hypothesis that 50% of first-time borrowers have the same size loans as other borrowers”. Less formally, we would say that “There is no evidence that one-half of first-time borrowers are significantly different in loan size from other borrowers”. Notice the length to which the conclusion goes to include all of the conditions that are attached to the conclusion. Statisticians, for all the criticism they receive, are careful to be very specific even when this seems trivial. Statisticians cannot say more than they know and the data constrain the conclusion to be within the metes and bounds of the data.
Exercise \(\PageIndex{3}\)
A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 104 students and 89 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.
Example \(\PageIndex{5}\)
Suppose a consumer group suspects that the proportion of households that have three or more cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test using 90% confidence. Their marketing people survey 150 households with the result that 43 of the households have three or more cell phones.
- Answer
-
Here is an abbreviated version of the system to solve hypothesis tests applied to a test on a proportions.
\[H_0 : P = 0.3 \nonumber\]
\[H_a : P \neq 0.3 \nonumber\]
\[n = 150\nonumber\]
\[P^{\prime}=\frac{x}{n}=\frac{43}{150}=0.287\nonumber\]
\[z_{obs}=\frac{P^{\prime}-P_{0}}{\sqrt{\frac{P_{0} (1-P_{0})}{n}}}=\frac{0.287-0.3}{\sqrt{\frac{.3(.7)}{150}}}=0.347\nonumber\]
At a confidence level of 90% we cannot reject the null hypothesis that the consumer group is correct.
Example \(\PageIndex{6}\)
In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. Explain why the significance level should be so low in terms of a Type I error.
- Answer
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We need to conduct a hypothesis test on the claimed cancer rate. Our hypotheses will be:
\(H_0: P \leq 0.00034\) \(H_a: P > 0.00034\)If we commit a Type I error, we are essentially accepting an incorrect claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.


7.18: Retail Information Systems
- Define retail information system and the data it stores
Retail information systems have evolved in similar fashion as business computing in general. More data has created the need for larger storage and faster processors. The need to give wider data access to more employees, so-called “data democratization,” has necessitated de-centralizing information platforms and increasing ease-of-use. We have seen platform evolution from mainframe systems to client/server to cloud and now to mobile platforms in retail information systems.
Today retail information systems (RIS) vary in platform, cost, and functionality–and range from simple to complex. Simple systems can support point-of-sale (POS) transactions and keep track of sales activity. Complex systems, designed for large enterprises, can manage all aspects of the business: POS, Supply Chain, Finance, HR, CRM and more. Whether simple applications or complex systems, modern retail information systems all utilize databases and provide access to stored data through Graphical User Interfaces (GUI).
POS informs retailers of the details of sales transactions: what item was sold, where the transaction occurred, at what price, what employee performed the sale, and information about the customer making the purchase. Supply chain management systems (SCM) track the origin of the product even before it arrives at store or warehouse (and will be discussed in more detail in the next section). Financial data systems provide management with data concerning the organizations profit and loss factors. Human resource systems (HRS) keep track of employees: status, title, employment type, salary, address, etc. Customer relation management systems (CRM) track customer information and will be discussed in a later section.
Contributors and Attributions
- Retail Information Systems. Authored by : Bob Danielson. Provided by : Lumen Learning. License : CC BY: Attribution
- Old fashioned cash register. Authored by : kdaubon. Provided by : Pixabay. Located at : https://pixabay.com/en/old-fashioned-cash-register-old-1546817/ . License : CC0: No Rights Reserved


2 .
Explain how pelvic dystocia can cause malpositioning of the fetal head and stalling of cervical dilation.
3 .
What are the contraindications to induction of labor?
4 .
How will the nurse prepare for the delivery of twins?
5 .
How can the nurse prepare the parents for delivery of an intrauterine fetal demise?
6 .
What nursing interventions are necessary for the laboring person with heart disease?
7 .
Describe possible labor complications associated with maternal musculoskeletal disorders.
8 .
How does the nurse prepare the person for an operative birth?
9 .
Explain placental abruption and its emergency status.
10 .
Discuss umbilical cord problems that indicate the need for a cesarean birth.
11 .
The nurse is caring for a 40-year-old person with preeclampsia during labor induction. The nurse sees bleeding at the IV site and the site where the lab drew blood this morning. What complication should the nurse predict and why?
12 .
What is the recommended course of action for the nurse in the case of end-stage prolonged fetal bradycardia during labor?
13 .
Describe the interventions used during a postpartum hemorrhage.
14 .
Explain how preeclampsia can cause neurologic dysfunction.


43.2A: External and Internal Fertilization
- Compare and contrast external and internal methods of fertilization
External Fertilization
External fertilization usually occurs in aquatic environments where both eggs and sperm are released into the water. After the sperm reaches the egg, fertilization can then take place. Most external fertilization happens during the process of spawning where one or several females release their eggs and the male(s) release sperm in the same area, at the same time. The release of the reproductive material may be triggered by water temperature or the length of daylight. Nearly all fish spawn, as do crustaceans (such as crabs and shrimp), mollusks (such as oysters), squid, and echinoderms (such as sea urchins and sea cucumbers). Pairs of fish that are not broadcast spawners may exhibit courtship behavior. This allows the female to select a particular male. The trigger for egg and sperm release (spawning) causes the egg and sperm to be placed in a small area, enhancing the possibility of fertilization.
External fertilization in an aquatic environment protects the eggs from drying out. Broadcast spawning can result in a greater mixture of the genes within a group, leading to higher genetic diversity and a greater chance of species survival in a hostile environment. For sessile aquatic organisms such as sponges, broadcast spawning is the only mechanism for fertilization and colonization of new environments. The presence of the fertilized eggs and developing young in the water provides opportunities for predation, resulting in a loss of offspring. Therefore, millions of eggs must be produced by individuals. The offspring produced through this method must mature rapidly. The survival rate of eggs produced through broadcast spawning is low.
Internal Fertilization
Internal fertilization occurs most often in land-based animals, although some aquatic animals also use this method. There are three ways that offspring are produced following internal fertilization: oviparity, ovoviparity, and viviparity.
In oviparity, fertilized eggs are laid outside the female’s body and develop there, receiving nourishment from the yolk that is a part of the egg. This occurs in most bony fish, many reptiles, some cartilaginous fish, most amphibians, two mammals, and all birds. Reptiles and insects produce leathery eggs, while birds and turtles produce eggs with high concentrations of calcium carbonate in the shell, making them hard. These animals are classified as oviparous.
In ovoviparity, fertilized eggs are retained in the female, but the embryo obtains its nourishment from the egg’s yolk; the young are fully developed when they are hatched. This occurs in some bony fish (such as the guppy, Lebistes reticulatus ), some sharks, some lizards, some snakes (such as the garter snake, Thamnophis sirtalis ), some vipers, and some invertebrate animals (such as the Madagascar hissing cockroach, Gromphadorhina portentosa ).
In viviparity, the young develop within the female, receiving nourishment from the mother’s blood through a placenta. The offspring develops in the female and is born alive. This occurs in most mammals, some cartilaginous fish, and a few reptiles, making these animals viviparous.
Internal fertilization has the advantage of protecting the fertilized egg from dehydration on land. The embryo is isolated within the female, which limits predation on the young. Internal fertilization also enhances the fertilization of eggs by a specific male. Even though fewer offspring are produced through this method, their survival rate is higher than that for external fertilization.
Key Points
- External fertilization is characterized by the release of both sperm and eggs into an external environment; sperm will fertilize the egg outside of the organism, as seen in spawning.
- Internal fertilization is characterized by sperm fertilizing the egg within the female; the three methods include: oviparity (egg laid outside female body), ovoviparity (egg held within female), and viviparity (development within female followed by live birth).
- Internal fertilization protects the fertilized egg or embryo from predation and harsh environments, which results in higher survival rates than can occur with external fertilization.
- Ovoviparity is characterized by an organism retaining a fertilized egg inside the body where development occurs and nourishment is received from the yolk.
- Viparity is characterized by an organism which has its young develop within the female and nourishment is received directly from the mother via a placenta.
Key Terms
- oviparous : egg-laying; depositing eggs that develop and hatch outside the body as a reproductive strategy
- viviparous : being born alive, as are most mammals, some reptiles, and a few fish (as opposed to being laid as an egg)
- ovoviparity : eggs are retained in the female, but the embryo obtains its nourishment from the egg’s yolk