Question

Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group 1) and 7 men (group 2) employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family. The results of the test are t = 2.02 with an associated P-value of 0.0352. The correct conclusion at α = 0.05 is to:______

I. reject the null hypothesisII. fail to reject the null hypothesisIII. conclude that women take a higher average number of personal time per year compared to men
a. I onlyb. both II and IIIc. III onlyd. II onlye. both I and III

Answer 1

Option E: I and III

Explanation:

The Human Resources Department believes that women tend to take less personal time than men because they tend to be the primary child care givers in the family. This will be the null hypothesis.

The correct conclusion at α = 0.05 is to reject the null as the p value 0.0352 is less than 0.05 thus we reject the null and conclude that women tend to take less personal time than men because they tend to be the primary child care givers in the family.

Answer 2

Both I and both III

Explanation:

For this discussion we know that the null hypothesis would be that women do not take more personal time than men, however after the study it is obtained with a significant p of 0.035, less than p 0.05, which leads us to take the correct option to discard the null hypothesis, taking option I, with the next step that is to conclude that women take a higher average of personal time per year compared to men option III, so the correct answer is E.