Question

A professor believes that students at her large university who exercise daily perform better in statistics classes. Since all students at the university are required to take Introduction to Statistics, she randomly selects 17 students who exercise daily and 22 students who exercise at most once per week. She obtains their scores in the final exam in Introduction to Statistics and finds that the students who did not exercise daily primarily produced scores in the 90s, with some scores in the 80s and a very few scores in the 70s and 60s. The students who did exercise daily also had a large number of scores in the 90s and an almost equal number in the 60s, with very few scores in between.

Would it be valid for the professor to use the independent-measures t test to test whether students at her large university who exercise daily perform better in statistics classes?

a. Yes, because the two populations from which the samples are selected have equal variances.
b. Yes, because none of the assumptions of the independent-measures t test are violated.
c. No, because the two populations studied are not independent.
d. No, because the two populations from which the samples are selected do not appear to be normally distributed.

Answer 1

d. No, because the two populations from which the samples are selected do not appear to be normally distributed.

Explanation:

First, the assumptions of an independent-measures t test are as follows:

1. The data is continuous

2. Only two groups are compared

3. The two groups should be independent

4. The groups should have equal variance

5. The data should be normally distributed

In this case, the 5th assumption has been violated because scores in the two samples are distributed in different ranges in two samples. So the outliers in the scores may be exist. Therefore, it would not be valid for the professor to use the independent-measures t test because the two populations from which the samples are selected do not appear to be normally distributed.