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