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

question 74

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 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. $$\begin{array} { r | r r r r r r r r } \text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\ \hline \text { Before } & 117.6 & 110.6 & 109.5 & 112 & 117.6 & 116.8 & 111.3 & 111.8 \\ \hline \text { After } & 118.2 & 109.3 & 107.1 & 112.8 & 115.8 & 116.9 & 107.7 & 107.9 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters? Use the P-value approach.

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Definitions:

Bond Discount Amortized

The process of gradually writing off the discount on bonds payable over the life of the bonds, affecting interest expense on the income statement.

Bond Premium Amortization

The process of gradually expensing the premium paid over the par value of a bond over its life.

Effective Yield

The total yield of a bond once all charges are factored in, expressed as an annual percentage.