Test the Given Claim About the Means of Two Populations

question 12

Essay

Test the given claim about the means of two populations. Assume that two dependent samples
have been randomly selected from normally distributed populations. A coach uses a new
technique to train gymnasts. 7 gymnasts were randomly selected and their competition scores
were recorded before and after the training. The results are shown below. $$\begin{array} { l | c c c c c c c } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \\\hline \text { Before } & 9.5 & 9.4 & 9.6 & 9.5 & 9.5 & 9.6 & 9.7 \\\hline \text { After } & 9.6 & 9.6 & 9.6 & 9.4 & 9.6 & 9.9 & 9.5\end{array}$$ Using a 0.01 level of significance, test the claim that the training technique is effective in raising
the gymnasts' scores. Include your null and alternative hypotheses, the test statistic, P-value or
critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your
answer.

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Definitions:

Achilles Tendon

A strong and fibrous tendon that connects the muscles in the back of your calf to your heel bone, crucial for walking, running, and jumping.

Common Bursae

Small fluid-filled sacs located near joints that reduce friction between bones and soft tissues, commonly found in the shoulder, elbow, hip, and knee.

Gastrocnemius

The large muscle in the calf of the leg.

Muscles Contract

The process by which muscle fibers shorten and generate force, typically in response to a signal from the nervous system.