Question 03) Suppose you wish to test the effect of Prozac on the well-being of depressed individuals using a standardized "well-being scale" that sums Likert-type items to obtain a score that could range from 0 to 20. Higher scores indicate greater well-being (that is, Prozac is having a positive effect). Patient ID 2 + 5 9 MoodPre 3 0 2 7 7 3 64 + MoodPost 5 1 LO 7 10 10 9 N 11 8 Has Prozac been effective? 1. Write down your hypothesis. 2. Write down the test statistic that you recommend using and find its value at a = = 0.05. 3. Define the rejection region for your test at a = 0.05, 4. Find the p-value. 5. What is your conclusion? 6. What is your recommended two-sided confidence interval? Report your upper and lower bounds' formula. 7. Report a two-sided confidence interval at a = 0.05. Question 04) Data measured on n=3,539 participants who attended the seventh examination of the Offspring in the Framingham Heart Study are shown below. Characteristic Women Men n X S n X S Systolic Blood Pressure 1,623 128.2 17.5 1,911 126.5 20.1 Suppose we now wish to assess whether there is a statistically significant difference in mean systolic blood pressure between men and women using a 5% level of significance. 1. Write down your hypothesis. 2. Write down the test statistic that you recommend using and find its value at a 3. Define the rejection region for your test. = 0.05. 4. Find the p-value. 5. What is your conclusion? 6. Given the large sample size (n>30), derive your conclusion based on a normal statistic test. 7. Define two-sided confidence intervals for both Z and T statistics, which one is wider? Why?