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 21.86 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.
a. Write the null and alternative hypotheses.
b. Based on the test statistic and its P-value, state your conclusion using a = .05.