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:

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Closing Entries

Entries in the journal made during the closing of an accounting period to move balances from transitory accounts to enduring accounts.

Fiscal Year

A one-year period that companies and governments use for financial reporting and budgeting, different from the calendar year.

Closing Entries

Journal entries made at the end of an accounting period to transfer temporary account balances to permanent accounts to prepare the books for the next period.