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. $$\begin{array}{l}
\begin{array} { c | c | c | c | c }
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}\\
\text { The ANOVA table output is shown here: }\\
\begin{array} { c | c | c | c | c | c }
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Batter } & 7 & 6227.4 & 946.77 & 39.70 & 0.0000 \
\text { Brand } & 3 & 4117.6 & 1372.54 & 57.55 & 0.0000 \
\text { Error } & 21 & 500.9 & 23.85 & & \
\text { Total } & 31 & 11245.9 & & &
\end{array}
\end{array}$$ Identify the test statistic that should be used for testing whether the average distance hit for the four brands of baseball bats differ.
A) 39.7
B) 23.85
C) 57.55
D) 0.0000

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. $$\begin{array}{l}
\begin{array} { c | c | c | c | c } 
\text { Batter } & \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } & \text { Brand 4 } \
\hline 1 & 307 & 315 & 300 & 275 \
2 & 310 & 317 & 305 & 285 \
3 & 335 & 335 & 330 & 302 \
4 & 325 & 328 & 320 & 300 \
5 & 300 & 305 & 295 & 270 \
6 & 345 & 350 & 340 & 310 \
7 & 312 & 315 & 308 & 300 \
8 & 298 & 302 & 295 & 288
\end{array}\\
\text { The ANOVA table output is shown here: }\\
\begin{array} { c | c | c | c | c | c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\hline \text { Batter } & 7 & 6227.4 & 946.77 & 39.70 & 0.0000 \
\text { Brand } & 3 & 4117.6 & 1372.54 & 57.55 & 0.0000 \
\text { Error } & 21 & 500.9 & 23.85 & & \
\text { Total } & 31 & 11245.9 & & &
\end{array}
\end{array}$$ Identify the test statistic that should be used for testing whether the average distance hit for the four brands of baseball bats differ.
A) 39.7
B) 23.85
C) 57.55
D) 0.0000

Quizplus · Accepted Answer

The test statistic for testing whether the average distance hit for the four brands of baseball bats differ is the F-value for the "Brand" source, which is 57.55.

Four Brands of Baseball Bats Were Tested to Determine Which