Write Hypotheses for the Two-Sample T-Test $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$

Write hypotheses for the two-sample t-test.
-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. $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } < 0$ .
B. $H _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } \neq 0$ .
C. $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } > 0$ .
D. $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0$ and $\mathrm { H } _ { \mathrm { A } } : \mu _ { 1 } - \mu _ { 2 } < 0$ .
E. None of the above.