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 in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below. $$\begin{array} { r | r r r r r r r r } \text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\ \hline \text { Before } & 109.7 & 112.3 & 109.5 & 118.3 & 111.1 & 120 & 117.1 & 114.6 \\ \hline \text { After } & 110.3 & 111 & 107.1 & 119.1 & 109.3 & 120.1 & 113.5 & 110.7 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters? Use the critical-value approach.

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Critical value Reject . At ...

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