Determine the null and alternative hypotheses for the proposed hypothesis test.
-A nutritionist wants to investigate whether her new diet will be effective in helping women aged 30-40 to lose weight. She will use a paired sample to determine whether the mean weight of Women before going on this diet is greater than the mean weight of women after being on this diet For two months.
A) Let

\mu _ { 1 }

denote the mean weight of women before going on this diet and let

\mu _ { 2 }

denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are

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

and

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

.
B) Let

\mu _ { 1 }

denote the mean weight of women before going on this diet and let

\mu _ { 2 }

denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are

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

and

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

.
C) Let

\mu _ { 1 }

denote the mean weight of women before going on this diet and let

\mu _ { 2 }

denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are

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

and

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

.
D) Let

\mu _ { 1 }

denote the mean weight of women before going on this diet and let

\mu _ { 2 }

denote the mean weight of women who have been on this diet for two months. The null and alternative hypotheses are

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

and

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

The Pooled T-Test Requires the Assumption That the Two Population

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