Problem 6. Hypothesis Testing for Mean with unknown variance (30-Year Fixed Mortgage rate): Rates on 30-year fixed mortgages continue to be at historic lows. According to Freddie Mac, the average rate for 30-year fixed loans in the last week of July 2020 was 2.99%. An economist wants to test if there is any change in the mortgage rates since then. She searches for 30-year fixed loans on google.com and reports the rates offered by 9 banks: 30-year mortgage rate (Aug 2020) 2.89 3.36 3.28 2.79 3.08 3.18 2.96 2.94 3.02 . Assume that rates are normally distributed.

(6.2) Challenging. Report the 90% confidence interval for the average mortgage rate. Use this confidence interval to confirm your conclusion in part (6.1).