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, which is given :

30-year mortgage rate (Aug 2020) 2.89 3.36 3.28 2.79 3.08 3.18 2.96 2.94 3.02 (6.3) Challenging. Finally, carry out a hypothesis test against the null that the average mortgage rate is at most 2.99%. Clearly state your hypotheses, the test statistic, the critical value, your decision rule and conclusion. Use a t-test and = 0.10. Does your conclusion change if you use = 0.05?