Data Were Collected on Annual Personal Time (In Hours) Taken $24.75$

Data were collected on annual personal time (in hours) taken by a random sample of 16 women (group1) 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 correct null and alternative hypotheses to test this belief are

A) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { A } : \mu _ { 1 } - \mu _ { 2 } < 0$ .
B) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { A } : \mu _ { 1 } - \mu _ { 2 } > 0$ .
C) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { A } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ .
D) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0$ and $H _ { A } : \mu _ { 1 } - \mu _ { 2 } < 0$ .
E) None of the above.