For each of the following situations, state whether the appropriate test would be a Independent Samples T test or Paired T Test, assuming the conditions are met to run these tests. Give the null and alternate hypotheses that would be used to test the claim using mathematical notation.
(a) Suppose you want to test your theory that "taking Aspirin regularly reduces blood pressure". To investigate your claim, you find 40 identical twin pairs (80 people) willing to participate in your study. You randomly assign one member of each pair to take aspirin every day for 2 months, and the other to take a placebo every day for 2 months. After 2 months, you measure the blood pressure of all 80 people. For each twin pair, you then compute the difference in blood pressure between treatments, calculated as the blood pressure of the twin taking the aspirin the blood pressure of the twin taking the placebo.
1. Which test is appropriate?
O Independent Samples T Test
O Paired T Test
2. What are the appropriate hypotheses?
O H0: μaspirin - μplacebo = 0 and Ha: μaspirin - μplacebo > 0
O H0: μd = 0 and Ha: μd < 0 where μd= mean difference in blood pressure (calculated as aspirin - placebo)
(b) A sociologist wants to test the theory that the number of serious relationships that men and women have before age 21 is different. She takes a SRS of 45 women and a SRS of 50 men between the ages of 21 and 25. The researcher determines the number of serious relationships each individual in her study had before the age of 21.
1. Which test is appropriate?O Independent Samples T TestO Paired T Test2. What are the appropriate hypotheses?O H0: μmen - μwomen = 0 and Ha: μmen - μwomen /= 0O H0: μd = 0 and Ha: μd > 0 where μd= mean difference in number of serious relationships before age 21 (calculated as men - women)