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

Question

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

Quizplus · Accepted Answer

The null hypothesis always specifies a statement of equality (e.g., $\mu_1 = \mu_2$), and the alternative hypothesis specifies the research hypothesis of interest, which in this case is that there is a difference ($\mu_1 \neq \mu_2$).

Determine the Null and Alternative Hypotheses for the Proposed Hypothesis μ1\mu _ { 1 }μ1​

Determine the Null and Alternative Hypotheses for the Proposed Hypothesis $\mu _ { 1 }$