QuestionUse a $t$-distribution to find a confidence interval for the difference in means $\mu_{d}=\mu_{1}-\mu_{2}$ using the relevant sample results from paired data. Assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using $d=x_{1}-x_{2}$.
A 95\% confidence interval for $\mu_{d}$ using the paired data in the following table: \begin{tabular}{l|ll} \hline Case & \begin{tabular}{l} Situation \\ 1 \end{tabular} & \begin{tabular}{l} Situation \\ 2 \end{tabular} \\ \hline 1 & 78 & 86 \\ 2 & 80 & 85 \\ 3 & 95 & 90 \\ 4 & 62 & 78 \\ 5 & 71 & 78 \\ 6 & 72 & 62 \\ 7 & 84 & 88 \\ 8 & 91 & 92 \\ \hline \end{tabular}
Give the best estimate for $\mu_{d}$, the margin of error, and the confidence interval. Enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places. best estimate $=$ $\square$ $-3.5$ margin of error = $\square$ $\square$ $-6.71$
The $95 \%$ confidence interval is to i 3.21 $\square$