Use the Wilcoxon Signed -Ranks Test to Test the Claim

question 8

Essay

Use the Wilcoxon signed -ranks test to test the claim that the matched pairs have differences that come from a
population with a median equal to zero. Eleven runners are timed at the 100-meter dash and are timed again
one month later after following a new training program. The times (in seconds) are shown in the table. Use
Wilcoxon's signed-ranks test and a significance level of 0.05 to test the claim that the training has no effect on the times. $$\begin{array} { | l l l l l l l l l l l l | } \hline \text { Before } & 12.1 & 12.4 & 11.7 & 11.5 & 11.0 & 11.8 & 12.3 & 10.8 & 12.6 & 12.7 & 10.7 \\\hline \text { After } & 11.9 & 12.4 & 11.8 & 11.4 & 11.2 & 11.5 & 12.0 & 10.9 & 12.0 & 12.2 & 11.1 \\\hline\end{array}$$

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Definitions:

Functional Magnetic Resonance Imaging (fMRI)

A neuroimaging technique that measures brain activity by detecting changes associated with blood flow.

Hemoglobin

A protein in red blood cells that carries oxygen from the lungs to the body’s tissues and returns carbon dioxide from the tissues back to the lungs.

Brain Activity

The functioning of the brain as it engages in various cognitive, sensory, and motor tasks, typically measured by various neuroimaging techniques.

Hormones

Chemical messengers produced by the endocrine glands that regulate various bodily functions and processes.