What is the smallest sample size required to obtain the desired margin of error? So let's just remind ourselves what the confidence interval will look like and what part of it is the margin of error and then we can think about what is her sample size that she would need. So she wants to estimate the true population proportion that favor a tax increase. She doesn't know what this is so she is going to take a sample size of size n and in fact this question is all about what n does she need in order to have the desired margin of error. Well whatever sample she takes there she's going to calculate a sample proportion and then the confidence interval that she's going to construct is going to be that sample proportion plus or minus critical value and this critical value is based on the confidence level. We'll talk about that in a second. What z-star, what critical value would correspond to a 95% confidence level times and then you would have times the standard error of her statistic and so in this case it would be the square root.