Determine the null and alternative hypotheses for the proposed hypothesis test.
-A researcher wants to use a paired sample to determine whether the mean number of hours spent exercising per week for married men differs from the mean number of hours spent exercising per Week for married women.
A) Let

\mu _ { 1 }

denote the mean number of hours spent exercising per week for married men and let

\mu _ { 2 }

denote the mean number of hours spent exercising per week for married women. The null and alternative hypotheses are

\mathrm { H } _ { 0 } : \mu _ { 1 } \neq \mu _ { 2 }

and

\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } = \mu _ { 2 }

.
B) Let

\mu _ { 1 }

denote the mean number of hours spent exercising per week for married men and let

\mu _ { 2 }

denote the mean number of hours spent exercising per week for married women. The null and alternative hypotheses are

\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }

and

\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 }

.
C) Let

\mu _ { 1 }

denote the mean number of hours spent exercising per week for married men and let

\mu _ { 2 }

denote the mean number of hours spent exercising per week for married women. The null and alternative hypotheses are

\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }

and

\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } > \mu _ { 2 }

.
D) Let

\bar { x } _ { 1 }

denote the mean number of hours spent exercising per week for married men and let

\bar { x } _ { 2 }

denote the mean number of hours spent exercising per week for married women. The null and alternative hypotheses are

\mathrm { H } _ { 0 } : \bar { x } _ { 1 } = \bar { x } _ { 2 }

and

\mathrm { H } _ { \mathrm { a } } : \bar { x } _ { 1 } \neq \bar { x } _ { 2 }

Suppose That You Want to Perform a Hypothesis Test to Compare

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