Question 1 n that the unusually large number of home runs that were hit was due

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Question 1 n 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 During the 1999 and 2000 baseball seasons, there was much s baseball is to launch the ball at a vertical surface with a known velocity L and measure the rat of the outgoing velocity VO o the ball to L The ratio O ,L ls 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 0.625 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.

Explanation / Answer

So sample size n = 40

Number of baseballs that are too lively (Means Coefficient of restitution exceeds 0.625) = 18

p^ = 18/40 = 0.450

95% confidence lower bound = p^ - Z95% sqrt[p^ *(1-p^)/N] = 0.45 - 1.645 * sqrt (0.45 * 0.55/40) = 0.321

p >= 0.321

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