Question

Theomect 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 V, and measure the ratio of the outgoing velocity Vo of the ball to V. The ratio R = Vo/V 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. 06248 0.6237 0.6118 0.6159 0.6298 0.6192 06520 06368 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 06351 0.6275 0.6261 0.6262 0.6262 0.6314 06128 0.6403 0.6521 0.6049 0.6170 0.6134 0.6310 0.60650.6214 0.6141 Suppose that any baseball that has a coefficient of restitution that exceeds 0.640 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. Round your answers to 3 decimal places. P= 025

Answer 1

The number of coefficients that are greater than 0.64 is 5.

DATE We arre exceed 0.640 considered given if coefficient of restitution 0.640 then the basellball is lively. let X be that are number of sampled baseball lively No. of obs. above o = 0.640 x Х = 5 n = 40 o's of Proportion Sample that are the baseballs the too lively is 0.125 Х 5 - P n 40 confidence bound is The 95% lower given by a LCB = Z4z (1-8) 우 n ZH2 1.96 oo LCB = 0.125 -1.96 0.125x0.875 40 0.0225