During the 1999 and 2000 baseball seasons, there was much speculation that the u

Question

During the 1999 and 2000 baseball seasons, there was much speculation that the unusually large number of home runs there 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 Vi and measure the ratio of the outgoing velocity Vo of the ball to Vi. The ratio R = Vo/Vi is called the coefficient of restitution. A batch of 40 baseballs were tested by throwing each ball from a pitching machine at an oak surface. The average coefficient of restitution was found to be x=.6373, with standard deviation s= .013. If the mean coefficient of restitution exceeds .635, then the population of balls from which the sample was taken will be too "lively", and considered unacceptable for play. Test the hypothesis that the balls in the sampled population are toodively using the 5% significance level. 8. (Continuation of 6.) Find the power of the test if the true mean coefficient of restitution is cqual to.638 (a) 0.426 (b) 0.574 (c) 0.737 (d) 0.569 (e) 0.403

Explanation / Answer

here std error =std deviation/(n)1/2 =0.013/(40)1/2 =0.002

for 0.05 level critical z=1.645

hence rejection region =0.635+1.645*0.002 =0.6384

hence power of the test =P(X>0.6384)=P(Z>(0.6384-0.638)/0.002)=P(Z>0.1853)=0.426

option A is correct

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