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Preliminary Data Analyses Indicates That Use of a Paired T-Test H0:μ1=μ2\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 H0:μ1=μ2\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.  Athlete  A  B  C  D  E  F  G  H  Before 117.6110.6109.5112117.6116.8111.3111.8 After 118.2109.3107.1112.8115.8116.9107.7107.9\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:

Classically Conditioned

Classically conditioned refers to a learning process in classical conditioning where a neutral stimulus becomes associated with a significant response through repeated pairings with a stimulus that inherently causes that response.

Romantic Comedy

A genre of movies that combines elements of romance and comedy, centering on two people as they navigate romantic entanglements.

Procedural Memory

A type of long-term memory that involves the ability to perform skills, operations, or actions.

Episodic Memory

The type of long-term memory that involves the recollection of specific events, situations, and experiences, including time and place contexts.

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