Test the Given Claim About the Means of Two Populations

question 57

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. $$\begin{array} { l | c c c c c c c } \text { Subject } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } \\\hline \text { Before } & 9.5 & 9.4 & 9.6 & 9.5 & 9.5 & 9.6 & 9.7 \\\hline \text { After } & 9.6 & 9.6 & 9.6 & 9.4 & 9.6 & 9.9 & 9.5\end{array}$$ 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:

Summary

A brief statement or account of the main points of something, often used to provide a quick understanding or overview.

Accounting Statements

Financial reports that provide a summary of a company’s financial condition, including income statement, balance sheet, and cash flow statement.

P/E Ratios

Price-to-Earnings Ratio, a measure of a company's current share price relative to its per-share earnings.

Quick Ratio

A financial metric that measures a company's ability to meet its short-term obligations with its most liquid assets.