In Example 9-6 we described how the “spring-like effect” in a golf club could be determined by measuring the coefficient of restitution (the ratio of the outbound velocity to the inbound velocity of a golf ball fired at the club head). Twelve randomly selected drivers produced by two club makers are tested and the coefficient of restitution measured. The data follow:
Club 1: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8562,
0.8123, 0.7976, 0.8184, 0.8265, 0.7773, 0.7871
Club 2: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465,
0.8244, 0.8014, 0.8309, 0.8405, 0.8256, 0.8476
(a) Is there evidence that coefficient of restitution is approximately normally distributed? Is an assumption of equal variances justified?
(b) Test the hypothesis that both brands of ball have equal mean coefficient of restitution. Use a = 0.05.
(c) What is the P-value of the test statistic in part (b)?
(d) What is the power of the statistical test in part (b) to detect a true difference in mean coefficient of restitution of 0.2?
(e) What sample size would be required to detect a true difference in mean coefficient of restitution of 0.1 with power of approximately 0.8?
(f) Construct a 95% two-sided CI on the mean difference in coefficient of restitution between the two brands of golf clubs.