Test the Given Claim About the Means of Two Populations

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