A Weight-Lifting Coach Claims That Weight-Lifters Can Increase Their Strength $\alpha$

Essay

A weight-lifting coach claims that weight-lifters can increase their strength by taking a certain supplement. To
test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The
results are listed below. Thirty days later, after regular training using the supplement, they are tested again.
The new results are listed below. Test the claim that the supplement is effective in increasing the athletesʹ
strength. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.05. $$\begin{array} { l | c c c c c c c c c } \text { Athlete } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Before } & 215 & 240 & 188 & 212 & 275 & 260 & 225 & 200 & 185 \\\hline \text { After } & 225 & 245 & 188 & 210 & 282 & 275 & 230 & 195 & 190\end{array}$$