Statistics, Assumptions underlying the independent-measures t test

Assumptions underlying the independent-measures t test

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 7s and 60s. The Students who did excercies 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-measure t test to test whether students’ at her large university who exercise daily perform better in statistics classes?

Choices:

Yes, because none of the assumptions of the independent-measures are violated.

No, because the two populations studied are not independent.

Yes, because the two populations from which the samples are selectee have equal variances.

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