answer. 3. [25 pts. ] A longitudinal study is performed to evaluate the efficacy of melatonin supplements for reducing sleeplessness. Sleep patterns for 10 subjects were recorded before and after taking supplements and the following data shows total number of poor-quality sleep during a 30 -day period: a) Compute a $95 \%$ confidence interval for the mean difference in poor-quality sleep hours. b) What is the optimal statistical method to evaluate whether melatonin improved sleep quality? Justify your c) Perform your statistical evaluation from 3(b). d) Interpret the outcomes of $3 (\mathrm{c})-$ do the results of $3C\mathrm{a})$ and $3C\mathrm{C})$ provide the same information? \begin{tabular}{]c|cc|} Thline & \multicolumn{2}{]c]}{ Poor-Quality Sleep (hrs) } \hline Subject # & Melatonin $^{-}$ & Melatonin $^{+}$ W Thline 1 & 17 & $5.7$ \hline 2 & $8.2$ & $6.5$ \hline 3 & $10.4$ & $3.4$ \hline 4 & $4.7$ & $2.9$ W \hline 5 & $5.8$ & $6.1$ \hline \end{tabular) \begin{tabular}{]c[CC] \hline & \multicolumn{2}{\c]}{ Poor-Quality Sleep (hrs) } \hline Subject # & Melatonin $^{-}$ & Melatonin $^{+}$ \hline 6 & $7.9$ & $0.7$ \hline 7 & $5.1$ & $2.0$ \hline 8 & $5.4$ & $4.7$ \hline 9 & $25.6$ & $10.1$ \hline 10 & $16.0$ & $5.6$ \hline \end{tabular) $$ SP.PC.135