Question

Data were collected on annual personal time​ (in hours) taken by a random sample of 16 women and 7 men 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 providers in the family. Why is the t​-test for two means appropriate in this​ situation? A. The samples of women and men are matched. B. The samples of women and men are independent. C. The samples of women and men are dependent. D. The observations are paired.

Answer 1

Option B The samples of women and men are independent.

Explanation:

The t-test for two means is comparing two independent sample means to a null hypothesis value. Unlike the paired t-test, the 2-sample t-test needs independent groups for each sample. Thus, the samples of women and men are independent.