In Recent Years a Controversy Has Arisen in Major League $\quad$

In recent years a controversy has arisen in major league baseball in the US. Some players have been accused of 'doctoring' their bats to increase the distance the ball travels. However, a physics professor claims that the effect of doctoring is negligible. A major league manager decides to test the professor's claim. He doctors two bats by inserting cork into one and rubber into another. He then tells five players on his team to hit a ball with an undoctored bat and with the doctored bats. The distances are measured, and are listed below. Do these data provide sufficient evidence at the 5% level of significance to refute the professor's claim? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Distance ball travels (feet) }$$\begin{array}{|c|c|c|c|}\hline \text { Player } & \text { Undoctored bat } & \text { Bat with cork } & \text { Bat with rubber } \\\hline 1 & 275 & 265 & 280 \\\hline 2 & 315 & 335 & 320 \\\hline 3 & 425 & 435 & 440 \\\hline 4 & 380 & 375 & 370 \\\hline 5 & 450 & 460 & 450 \\\hline\end{array}$