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 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. If the mean coefficient of restitution exceeds 0.635, the population of balls from which the sample has been taken will be too "lively" and considered unacceptable for play.
(a) Formulate an appropriate hypothesis testing procedure to answer this question.
(b) Test these hypotheses using the data and draw conclusions, using α = 0.01.
(c) Find the P-value for this test.
(d) You found a 99% confidence interval on the mean coefficient of restitution. Does this interval, or a one-sided CI, provide additional useful information to the decision maker? Explain why or why not.