Assignment Problem: During the 1999 and 2000 baseball seasons, there was much speculation that the unusually large number of home runs that were hit was due at least in part to a livelier ball. One way to test the "liveliness" of a baseball is to launch the ball at a vertical surface with a known velocity VL and measure the ratio of the outgoing velocity VO of the ball to VL. The ratio R = VO/VL is called the coefficient of restitution. Following are measurements of the coefficient of restitution for 40 randomly selected baseballs. The balls were thrown from a pitching machine at an oak surface.
| 0.6248 |
0.652 |
0.6226 |
0.623 |
0.6237 |
0.6368 |
0.628 |
0.6131 |
| 0.6118 |
0.622 |
0.6096 |
0.6223 |
0.6159 |
0.6151 |
0.63 |
0.6297 |
| 0.6298 |
0.6121 |
0.6107 |
0.6435 |
0.6192 |
0.6548 |
0.6392 |
0.5978 |
| 0.6351 |
0.6128 |
0.6134 |
0.6275 |
0.6403 |
0.631 |
0.6261 |
0.6521 |
| 0.6065 |
0.6262 |
0.6049 |
0.6214 |
0.6262 |
0.617 |
0.6141 |
0.6314 |
(a) Is there evidence to support the assumption that the coefficient of restitution is normally distributed? Use α = 0.01
(b) Does the data support the claim that the mean coefficient of restitution of baseballs exceeds 0.623? Use the relevant test statistic approach to support your response, assuming α = 0.01
(c) What is the P-value of the test statistic computed in part (b)?
(d) Compute the power of the test if the true mean coefficient of restitution is as high as 0.63.
(e) What sample size would be required to detect a true mean coefficient of restitution as high as 0.63 if we wanted the power of the test to be at least 0.80?