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 €œliveliness€ 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.

(a) Is there evidence to support the assumption that the coefficient of restitution is normally distributed?
(b) Find a 99% CI on the mean coefficient of restitution.
(c) Find a 99% prediction interval on the coefficient of restitution for the next baseball that will be tested.
(d) Find an interval that will contain 99% of the values of the coefficient of restitution with 95% confidence.
(e) Explain the difference in the three intervals computed in parts (b), (c), and (d).

0.6248 0.6237 0.6118 0.6159 0.6298 0.6192 0.6520 0.6121 0.6368 0.6220 0.6151 0.6548 0.6226 0.6280 0.6096 0.6300 0.6107 0.6392 0.6230 0.6131 0.6223 0.6297 0.6435 0.5978 0.6351 0.6275 0.6262 0.6261 0.6262 0.6314 0.6128 0.6403 0.6521 0.6049 0.6170 0.6141 0.6134 0.6310 0.6065 0.6214