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Chapter $16$$\newline$- ($20$ points) Question $1$ : In order to test a theory that coffee consumption can have an effect on test scores, a researcher conducts a study on a group of adults. Each is given a test. Then for one week, each subject is required to consume a certain amount of coffee; then he or she is retested. The results are shown here.$\newline$\begin{tabular}{c|c}$\newline$\hline Score Before & Score After \\$\newline$\hline $109$ & $106$ \\$\newline$$116$ & $123$ \\$\newline$$123$ & $122$ \\$\newline$$114$ & $119$ \\$\newline$$107$ & $106$ \\$\newline$$105$ & $107$ \\$\newline$$115$ & $114$ \\$\newline$$95$ & $98$ \\$\newline$$111$ & $95$ \\$\newline$$98$ & $97$ \\$\newline$\hline$\newline$\end{tabular}$\newline$$1$. Test the claim that coffee improves test score. Use WRS and $\alpha$ $=0.01$.$\newline$- Solution :