Question6.156 Juvenile Diabetes Treatment Exercise 2.22 introduces a study examining the effectiveness of the drug teplizumab at delaying or preventing the onset of juvenile diabetes (also called Type 1 diabetes). The results are shown in Table 6.4. a. Using $\widehat{p}_{1}$ to represent the proportion in the control group who developed diabetes and $\widehat{p}_{2}$ to represent the proportion in the teplizumab group who developed diabetes, find the sample difference in proportions, $\widehat{p}_{1}-\widehat{p}_{2}$. b. Find a $99 \%$ confidence interval for the difference in proportions $p_{1}-p_{2}$. c. What is the best estimate for the difference in proportions? What is the margin of error for this estimate? d. Can we be confident, at the $99 \%$ level, that the new drug teplizumab is more effective than the control?
TABLE 6.4 Juvenile diabetes treatment \begin{tabular}{|l|c|c|c|} \hline & Diabetes & No diabetes & Total \\ \hline Teplizumab & 16 & 22 & 38 \\ \hline Control & 26 & 12 & 38 \\ \hline Total & 42 & 34 & 76 \\ \hline \end{tabular}