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.
$\begin{array} { l | c c c c c } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline \text { Before } & 71 & 66 & 67 & 77 & 75 \\\hline \text { After } & 75 & 75 & 65 & 80 & 87\end{array}$
Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math 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.