Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. $$\begin{array}{l}
\begin{array} { c | c | c | c | c }
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}\\
\text { The ANOVA table output is shown here: }\\
\begin{array} { c | c | c | c | c | c }
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Batter } & 7 & 6227.4 & 946.77 & 39.70 & 0.0000 \
\text { Brand } & 3 & 4117.6 & 1372.54 & 57.55 & 0.0000 \
\text { Error } & 21 & 500.9 & 23.85 & & \
\text { Total } & 31 & 11245.9 & & &
\end{array}
\end{array}$$ Based on the p-value for this test, make the proper conclusion about the treatments in this experiment.
A) There is sufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the eight batters.
B) There is sufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the four brands of baseball bats.
C) There is insufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the eight batters.
D) There is insufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the four brands of baseball bats.

Question

Four brands of baseball bats were tested to determine which bat allowed hitters to hit a baseball farthest. Eight different batters were thrown 25 pitches while hitting with each of the four bats (assigned in random order). The average distance of the five longest hits using each bat is shown in the table below. The goal is to determine if the average hit distance differs for the four brands of baseball bats. $$\begin{array}{l}
\begin{array} { c | c | c | c | c } 
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}\\
\text { The ANOVA table output is shown here: }\\
\begin{array} { c | c | c | c | c | c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Batter } & 7 & 6227.4 & 946.77 & 39.70 & 0.0000 \
\text { Brand } & 3 & 4117.6 & 1372.54 & 57.55 & 0.0000 \
\text { Error } & 21 & 500.9 & 23.85 & & \
\text { Total } & 31 & 11245.9 & & &
\end{array}
\end{array}$$ Based on the p-value for this test, make the proper conclusion about the treatments in this experiment.
A) There is sufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the eight batters.
B) There is sufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the four brands of baseball bats.
C) There is insufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the eight batters.
D) There is insufficient evidence (at ? = 0.01) to indicate differences among the mean distances for the four brands of baseball bats.

Quizplus · Accepted Answer

The p-value for the Brand effect is 0.0000, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to indicate differences among the mean distances for the four brands of baseball bats.

Four Brands of Baseball Bats Were Tested to Determine Which