You are still upset because your roommate takes pretty long showers, and this reflects negatively on your water bill. You think that their showers last on average 20 minutes. They think you are exaggerating. You record the duration of 36 random showers they take. They have a mean of 19 minutes and a standard deviation of 3.55 minutes. a) [3 points] Define the parameter of interest and the appropriate null and alternative hypotheses. b) [3 points] State and check if the assumptions needed for conducting the appropriate hypothesis test are satisfied. c) [2 points] Define the appropriate test statistic and calculate its value. d) [3 points] Calculate the p-value. (Indicate the correct degrees of freedom. You can indicate an approximate p-value or a range if needed.). e) [2 points] Write a conclusion. Use significance level 0.1.
