91Ó°ÊÓ

Eight golfers were asked to submit their latest scores on their favorite golf courses. These golfers were each given a set of newly designed clubs. After playing with the new clubs for a few months, the golfers were again asked to submit their latest scores on the same golf courses. The results are summarized below. $$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \text { Golfer } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Own clubs } & 77 & 80 & 69 & 73 & 73 & 72 & 75 & 77 \\ \hline \text { New clubs } & 72 & 81 & 68 & 73 & 75 & 70 & 73 & 75 \\ \hline \end{array}$$ a. Compute \(\bar{d}\) and \(s_{d}\). b. Give a point estimate for \(\mu_{1}-\mu_{2}-\mu_{\mathrm{d}}\). c. Construct the \(99 \%\) confidence interval for \(\mu_{1}-\mu_{2}-\mu_{\mathrm{d}}\) from these data. d. Test, at the \(1 \%\) level of significance, the hypothesis that on average golf scores are lower with the new clubs.