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

question 93

Multiple Choice

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

---

Definitions:

Continuous

Refers to data or a variable that can take on any value within a given range and is not restricted to specific separated values.

Scatterplot

A graphical representation of the relationship between two variables, showing how one variable is affected by the other.

Strength

Often used in the context of correlation, indicating the degree of association between two variables.

Relationship

The manner in which multiple concepts, objects, or individuals are linked, or the condition of being linked.