QuestionYou wish to test the following claim (Ha) at a significance level of $a=0.001$. For the context of this problem, $\mu \mathrm{d}=\mu 2-\mu 1$ where the first data set represents a pre-test and the second data set represents a post-test. Ho: $\boldsymbol{\mu d}=0$ Ha: $\boldsymbol{d}$ d>0 You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data: \begin{tabular}{|l|l|} \hline pre-test & post-test \\ \hline 56.1 & 59.3 \\ \hline 55.4 & 64.3 \\ \hline 43.3 & 44.8 \\ \hline 49.4 & 62.6 \\ \hline 51 & 49.6 \\ \hline 49.1 & 53.7 \\ \hline 49.9 & 47.7 \\ \hline 52.6 & 38 \\ \hline 52.1 & 53.6 \\ \hline 50.3 & 42.5 \\ \hline 47.4 & 37.1 \\ \hline 52.6 & 44.8 \\ \hline 50.4 & 67.9 \\ \hline 50.6 & 25.8 \\ \hline 46.6 & 56.2 \\ \hline 48.7 & 51.9 \\ \hline 45.6 & 33.8 \\ \hline 50.6 & 54.2 \\ \hline 46.1 & 68.2 \\ \hline 47.1 & 42.8 \\ \hline \end{tabular}
What is the test statistic for this sample?