Test the Given Claim About the Means of Two Populations

question 14

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:

Slotting

The activity of determining the most efficient placement for goods within a warehouse to optimize picking and storage.

Materials-Handling

The oversight of transporting, securing, storing, and regulating materials and items from the start of production, through storage and distribution, to the end use and disposal phase.

Space Efficiency

The effective use of physical space in facilities or buildings, aimed at maximizing utility and minimizing waste or overcapacity.

Product Handling Processes

The series of actions or steps taken to manage the physical movement and storage of products, from raw materials to finished goods, within the supply chain.