Question

You decide to test the hypothesis that people who walk to work will have lower blood pressure than those who drive to work. There is a large body of research indicating that walking for exercise does tend to reduce blood pressure. You place an advertisement in the newspaper asking for people to come in for a “free medical consultation”. During their visit, your research assistants asks various questions, provides basic health advice, and also takes their blood pressure. One of the questions asks how far the person to drives to work. You take everyone who drives less than 2 km and ask them to walk to work for the next 8 weeks. You then bring them and take their blood pressure again.

1. What would be the appropriate hypothesis test in this situation?  
2. Why?   Provide enough information to exclude all other possible hypothesis tests?

Answer 1

Answer : This is the case of " Paired t-test" .

Reason : Possible hypothesis that can be thought of for this data are Paired t-test and Two-Sample Independent t-test.

Now before getting to a conclusion, let us first list down the most important conditions (other than normality conditions) required for each of the above two tests. Thus,
In order to conduct a paired t-test, some important conditions are needed to be met and they are :
1) The sample data points must remain same in the before and after case i.e. same individual must be tested in the after case who has been tested in before case.
2) The total number of sample points must also remain same in the before and after case.

And the condiions required to conduct a Two-Sample Independent t-test. are :
1) The sample data points must be different in the before and after case i.e. same individual cannot be tested in the after case who has been tested in before case.
2) The before and after case sample data must be independent of each other.
3) Here, the total number of sample points can/cannot be same in the before and after case.

Since the data points (i.e. the individuals ) are not independent and all the above conditions mentioned in the Paired t-test are met by the case mentioned in the question above, thus this is the case of Paired t-test.

Hope this answers your query!