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

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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Critical value Do not reje...

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