5. (20 points) Suppose a medical researcher wants to know if a new drug lowers blood cholesterol levels. He randomly assigns 9 patients to a group which will take the new drug for 30 days, and he randomly assigns 9 more patients to another group which will take a placebo (such as a sugar pill) for 30 days. At the end of the 30 days, all 18 patients come back to have their blood glucose levels tested. The change in the blood glucose levels for each person is presented in the table below. At the bottom of the table, I also give you the mean and standard deviation for the Placebo group, the New Drug group, and the difference between the Placebo group and New Drug group values for the it person (i.e. the last column is the difference between the first and second columns). You may not need all of the columns in order to answer this question. Note that the values shown are positive because that is the amount that the blood cholesterol levels decreased. We want to show that the new drug has a larger numerical value below than the placebo. Units are in mg / dL. Placebo New Drug New Drug Placebo Person 1 3.7 7.5 3.8 Person 2 4.6 9.0 4.4 Person 3 5.5 9.3 3.8 Person 4 5.7 10.2 4.5 Person 5 6.0 10.2 4.2 Person 6 6.0 11.2 5.2 Person 7 6.4 11.2 4.8 Person 8 6.5 11.7 5.2 Person 9 7.4 14.6 7.2 5.76 10.54 4.79 1.09 2.00 1.04 Part 1: Testing the assumption of equal variances a. (2 points) Write the null and alternative hypothesis. b. (3 points) Calculate the Feat value. c. (2 points) Calculate the Forit value. Show your code. d. (3 points) Provide a complete conclusion and interpretation of your results. Part 2: Testing whether the mean of the new drug group is greater than the mean of the placebo group. e. (2 points) Write the null and alternative hypothesis. . (3 points) Calculate the trate value. g. (2 points) Calculate the terit value. Show your code. h. (3 points) Provide a complete conclusion and interpretation.6. [10 points) Revisit the data from Question {again Suppose that instead of using 9 different patients for each group at we had randomly assigned a patient to either the placebo group or the new drug group for 30 days and then, after 30 days, given the patient the other treatment [I'm not saying this is a smart idea, by the way]. What I am trying to get across is that the researchers went back and resampled the same patients, and they are interested in the difference between the two measures. Using the appropriate data in Question 2, please complete this t-test for the comparison of the difference between the New Drug and Placebo means. We still want to test if the New Drug group has a larger mean. a. [2 points) What are the null and alternative hypotheses? b. [3 points) What is the talk value? c. [2 points) What is the rm: value? Show your code. d. [3 points) Provide a complete conclusion and interpretation