Question

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.

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.
Which test is appropriate?
A. Independent Samples T Test
B. Paired T Test
What are the appropriate hypotheses?
A. H0: μaspirin - μplacebo = 0 and Ha: μaspirin - μplacebo > 0
B. H0: μd = 0 and Ha: μd < 0 where μd= mean difference in blood pressure (calculated as aspirin - placebo)

Answer 1

B. Paired T Test

B. H0: μd = 0 and Ha: μd < 0 where μd= mean difference in blood pressure (calculated as aspirin - placebo)

Explanation:

As the experiment is based on the difference between the results of a pair, the most appropiate test is a paired t-test.

If the 80 people group had been dividided in 2 and then compare the means for each group, it would have been a independent samples t-test.

For each pair, a variable d (for difference) is calculated and used as the outcome sample to perform the test.

Then, the null hypothesis will state that the population mean for this difference is not significantly different from 0, and the alternative hypothesis claiming it is signficant different from 0.

The sample means for the treatment group and the placebo is not individually calculated, as only the difference for each pair is used as sample in a paired t-test.