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

Answer 1

The answer is "No, because the two populations from which the samples are selected do not appear to be normally distributed.

Explanation:

The following are the assumptions of the two-sample t-test:

1. The variables are meant to be categorical, for the independent sampleorsample or group there should be no relationship between the subjects in each sample. It implies that subject in one group cannot be also in the second group. Hence, no one group orsample can influence the other group.

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

2. The samples are meant to be drawn randomly and representative of population.

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

4. Homogeneity of variances. That is, the variance should be approximately equal across groups.

5. There should be no outliers.

Therefore, in this scenario the sample sizes are only provided and the scores of two samples looks not be normally distributed due to the fact that the scores are distributed in different ranges in two samples. Hence, the outliers in the scores may exist. Therefore, the answer is “No, because the two populations from which the samples are selected do not appear to be normally distributed”.

Answer 2

The correct answer is the second option: "no, because the two populations from which the samples are drawn do not appear to be normally distributed"

Explanation:

As explained , the two distributions do not appear to be normally distributed

It states that the first group has the following pattern of scores:

Few scores in 90's

few in 80's

very few scores in 70's and 80's .

For second group:

Large number of scores in 90's

Large number in 60's

few in 70's and 80's

This distribution curve is U shaped , hence it is not normal .

Thus we cannot apply the 2 independent sample T test on it

Hence the correct answer choice is the second option , "no, because the two populations from which the samples are drawn do not appear to be normally distributed"