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

question 75

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 $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-A coach uses a new technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores were recorded before and after the training. The results are shown below. $$\begin{array} { c | r r r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Before } & 9.6 & 9.4 & 9.7 & 9.5 & 9.4 & 9.4 & 9.6 \\ \hline \text { After } & 9.7 & 9.6 & 9.7 & 9.4 & 9.5 & 9.7 & 9.4 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the training technique is effective in raising scores? Use the P-value approach.

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Definitions:

Transferability

The quality of being able to be legally transferred from one owner to another, such as property, titles, or financial instruments.

Unanimous Vote

A vote in which all members of a decision-making body agree and there are no dissenting opinions.

Winding Up

The process of settling the accounts and liquidating the assets of a company for the purpose of distributing the proceeds to claimants and shutting down the company permanently.

Implied Authority

The power of an agent to perform acts that are reasonably necessary to accomplish the purpose of an agency, even if not explicitly authorized.