Consider the following set of salary data: $\begin{array}{lrr} \hline & \text { Men (1) } & \text { Women (2) } \ \hline \text { Sample Size } & 100 & 80 \ \text { Mean } & \$ 12,850 & \$ 13,000 \ \text { Standard Deviation } & \$ 345 & \$ 500 \ \hline \end{array}$ To determine if women have a higher mean salary than men, we would test: A) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ B) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 } = 0$ C) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { a } : \mu _ { 1 } - \mu _ { 2 } 0$ D) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 }

Question

Consider the following set of salary data: $\begin{array}{lrr}
\hline & \text { Men (1) } & \text { Women (2) } \
\hline \text { Sample Size } & 100 & 80 \
\text { Mean } & \$ 12,850 & \$ 13,000 \
\text { Standard Deviation } & \$ 345 & \$ 500 \
\hline
\end{array}$

To determine if women have a higher mean salary than men, we would test:
A) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 } \neq 0$
B) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 } = 0$
C) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { a } : \mu _ { 1 } - \mu _ { 2 } > 0$
D) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ vs. $H _ { \mathrm { a } } : \mu _ { 1 } - \mu _ { 2 } < 0$

Quizplus · Accepted Answer

To test if women have a higher mean salary than men, the alternative hypothesis should indicate that the mean salary of women ($\mu_2$) is greater than that of men ($\mu_1$), which translates to $\mu_1 - \mu_2 < 0$.

Consider the Following Set of Salary Data To Determine If Women Have a Higher Mean Salary Than