Assumptions underlying the independent-measures t test A professor believes that

Question

Assumptions underlying the independent-measures t test

A professor believes that students at his large university who exercise daily perform better in statistics classes. Since all students at the university are required to take Introduction to Statistics, he randomly selects 17 students who exercise daily and 22 students who exercise at most once per week. He 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 his large university who exercise daily perform better in statistics classes? No, because the two populations studied are not independent. Yes, because the two populations from which the samples are selected have equal variances. Yes, because none of the assumptions of the independent-measures t test are violated. No, because the two populations from which the samples are selected do not appear to be normally distributed.

Explanation / Answer

Assumptions of the two-sample t-test is given below:

1. The variables should be categorical, for the independent sample/group there is no relationship between the subjects in each sample, it means that subject in one group cannot be also in the second group. And no one group/sample can influence the other group.

2. The samples should be drowning randomly and representative of population.

3. The plot of the data should be followed to the normal distribution

4. Homogeneity of variances (Variance approximately equal across groups).

5. No outliers.

Thus, in this case the sample sizesare only provided and the scores of two samples looks not be normally distributed becase scores are distributed in different ranges in two samples. So the outliers in the scores may be exist. Hence, it can say that “No, because the two populations from which the samples are selected do not appear to be normally distributed”.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.