Some students live either in apartments or apartment-style dorms on campus complete with a full kitchen. For students who live in these types of places and who enjoy cooking, they often eat all or most of their evening meals at home. For the purposes of this project the student wants to measure how long it takes them to cook dinner. It is conjectured that the mean time that it takes the student to prepare dinner, from gathering ingredients to putting it on a plate, will be 20 minutes. A simple random sample of 36 days was selected, and the time it took the student to cook/prepare the food each evening was recorded. The data is recorded below.

7.66 25.66 31.26 4.42 23.71 36.78 10.28 18.37 4.18 12.93 3.38 9.60 4.48 38.40
17.42 5.38 45.88 14.72 19.37 20.53 6.48 28.92 7.60 4.26 7.68 27.33 23.92 5.56
30.32 12.05 13.82 18.20 5.12 7.23 4.03 1.07

Required:
a. Using the correct statistical notation/symbol, what is the hypothesis that is made in the paragraph above?
b. Use the hypothesis stated in question 1 as the null hypothesis, and for the alternative hypothesis we want to test to see if the mean time that it takes the student to prepare dinner is different from 20 minutes. Write these two hypotheses in statistical notation.
c. Discuss the assumptions required to test the hypothesis in question 2, and whether they are satisfied in this case.