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 and measure the ratio of the outgoing velocity of the ball to . The ratio 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 0.6237 0.6118 0.6159 0.6298 0.6192 0.6520 0.6368 0.6220 0.6151 0.6121 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 0.6261 0.6262 0.6262 0.6314 0.6128 0.6403 0.6521 0.6049 0.6170 0.6134 0.6310 0.6065 0.6214 0.6141
Suppose that any baseball that has a coefficient of restitution that exceeds 0.630 is considered too lively.
Based on the available data, what proportion of the baseballs in the sampled population are too lively?
Find a 95% lower confidence bound on this proportion. Assume population is approximately normally distributed.
