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

question 7

Multiple Choice

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A pharmaceutical company wants to determine whether its new antianxiety medication has any effect on resting pulse rate. They will use a paired sample to determine whether the mean resting
Pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate
For adults who are taking the antianxiety medication.

• A) Let \(\mu _ { 1 }\) denote the mean resting pulse rate for adults not taking the antianxiety medication and let \(\mu _ { 2 }\) denote the mean resting pulse rate for adults who are taking the antianxiety medication. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 }\).
• B) Let \(\mu _ { 1 }\) denote the mean resting pulse rate for adults not taking the antianxiety medication and let \(\mu _ { 2 }\) denote the mean resting pulse rate for adults who are taking the antianxiety medication. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } > \mu _ { 2 }\).
• C) Let \(\mu _ { 1 }\) denote the mean resting pulse rate for adults not taking the antianxiety medication and let \(\mu _ { 2 }\) denote the mean resting pulse rate for adults who are taking the antianxiety medication. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } \neq \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } = \mu _ { 2 }\).
• D) Let \(\bar { x } _ { 1 }\) denote the mean resting pulse rate for adults not taking the antianxiety medication and let \(\bar { x } _ { 2 }\) denote the mean resting pulse rate for adults who are taking the antianxiety medication. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \overline { \mathrm { x } } _ { 1 } = \overline { \mathrm { x } } _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \overline { \mathrm { x } } _ { 1 } \neq \overline { \mathrm { x } } _ { 2 }\).

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Definitions:

Random Sample

A subset of individuals chosen from a larger set where each individual has an equal chance of being selected.

After-School Program

Educational and recreational activities organized for children after the regular school day has ended, often aimed at furthering learning and social development.

Causation

The relationship between cause and effect where one event (the cause) is understood to be responsible for the occurrence of another event (the effect).

Correlation

A measure of the relationship between two variables or sets of data.