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

question 11

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. $$\begin{array} { c | r r r r r r r } \text { Subject } & \text { A } & \text { B } & C & \text { D } & \text { E } & \text { F } & \text { G } \\ \hline \text { Before } & 9.7 & 9.7 & 9.4 & 9.6 & 9.7 & 9.7 & 9.4 \\ \hline \text { After } & 9.8 & 9.9 & 9.4 & 9.5 & 9.8 & 10 & 9.2 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the training technique is effective in raising scores? Use the critical-value approach.

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Definitions:

Not-Invented-Here Problem

A form of bias where individuals or organizations favor internally developed products or ideas over those originating externally.

Hoarding Of Expertise

The practice of individuals or groups within an organization deliberately keeping knowledge or skills to themselves to maintain a competitive advantage.

Knowledge Transfer

The process of sharing or disseminating knowledge from one part of an organization to another, or from one organization to another.

Personal Control

An individual's belief in their ability to influence events and their outcomes, often related to personal responsibility and autonomy.