Preliminary Data Analyses Indicates That Use of a Paired T-Test $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

question 16

Essay

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-The table below shows the weights, in pounds, of seven subjects before and after following a particular diet for two months. $$\begin{array} { c | r r r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Before } & 196 & 187 & 177 & 161 & 197 & 168 & 154 \\ \hline \text { After } & 189 & 178 & 175 & 166 & 183 & 170 & 142 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the diet is effective in reducing weight? Use the critical-value approach.

---

Definitions:

Ostracism

The social or psychological exclusion or rejection of an individual by a group, affecting the individual's behavior and mental health.

Excluded

Being intentionally left out or omitted from a group or an activity.

Grit

A psychological trait based on an individual's passion for a particular long-term goal coupled with a powerful motivation to achieve their respective objective.

Emotional Pain

Emotional pain is a deeply unpleasant psychological response that can result from a variety of life events, including loss, rejection, or disappointment.