Suppose you have a random sample from a normal distribution. Using this sample, you've estimated the sample mean to be 7.5. Your sample size is 25, and you've estimated the sample standard deviation to be 3.
a) Calculate the 90% confidence interval on the estimated sample mean.
b) Calculate the 99% confidence interval. Why is this interval larger?
c) Explain why this confidence interval would shrink if your sample size was 100 (there are two reasons).