```python
import matplotlib.pyplot as plt
import scipy.stats as st
import seaborn as sns
import pandas as pd
from scipy.stats import norm, uniform, expon, t
from scipy.integrate import quad
from sympy.solvers import solve
from sympy import Symbol
import numpy as np
from pandas import Series, DataFrame
```


```python
fuellungen = Series([71, 69, 67, 68, 73, 72, 71, 71, 68, 72, 69, 72])
```


```python
fuellungen.mean()
```




    70.25




```python
fuellungen_standardisiert = fuellungen
```


```python
norm.ppf(q=[0.05,0.95], loc=70, scale=1.5/np.sqrt(12))
```




    array([69.28775749, 70.71224251])




```python
np.sqrt(12)*((70.25-70)/1.5)
```




    0.5773502691896257




```python
norm.ppf(q=0.05)
```




    -1.6448536269514729



# 6.2


```python
fuellungen2 = Series([71, 69, 67, 68, 73, 72, 71, 71, 68, 72, 69, 72])
```


```python
fuellungen.mean()
```




    70.25




```python
t.ppf(q=[0.05], df=fuellungen2.size-1, loc=70, scale=fuellungen2.std()/np.sqrt(fuellungen2.size))
```




    array([68.98397389])




```python

```




    1.9598237397554634



# 6.3


```python
norm.ppf(q=[0.95], loc=200, scale=10/np.sqrt(16))
```




    array([204.11213407])




```python
norm.cdf(x=205, loc=200, scale=10/np.sqrt(16))
```




    0.9772498680518208




```python
norm.cdf(x=200, loc=200, scale=10/np.sqrt(16))
```




    0.5




```python
t.ppf(q=[0.95], df=16-1, loc=200, scale=10/np.sqrt(16))
```




    array([204.38262589])




```python
t.cdf(x=200, loc=200, df=16-1, scale=10/np.sqrt(16))
```




    0.5




```python
st.ttest_1samp()
```

f15c46f57dfad8f14ae61968667241ee21071b53
ipynb
Jupyter Notebook
Lernphase/SW06/Aufgaben.ipynb
florianbaer/STAT
7cb86406ed99b88055c92c1913b46e8995835cbb
MIT
Lernphase/SW06/Aufgaben.ipynb
florianbaer/STAT
7cb86406ed99b88055c92c1913b46e8995835cbb
MIT
Lernphase/SW06/Aufgaben.ipynb
florianbaer/STAT
7cb86406ed99b88055c92c1913b46e8995835cbb
MIT
Qwen/Qwen-72B
1. YES
2. YES