Studies have shown that humans complete a 1 mile run in an average of 12.2 minutes. There is a separate group of 30 who complete a 1 mile run with an average of 8.67 minutes with a standard deviation of 0.33 minutes.
a- Using a 0.05 significance level, test the claim that the population mean is different than 12.2 minutes based on the sample given.
b- Construct a 99% confidence interval estimate of the mean time.