The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the legendary champion, Byron Nelson. Ten randomly selected balls of two brands are tested and the overall distance measured. Assume that the variances are equal. The data follow:

Brand 1: 275, 286, 287, 271, 283, 271, 279, 275, 263, 267
Brand 2: 258, 244, 260, 265, 273, 281, 271, 270, 263, 268.

a. Is there evidence that overall distance is approximately normally distributed? Is an assumption of equal variances justified?
b. Test the hypothesis that both brands of ball have equal mean overall distance. Use α = 0.05. What is the P-value?
c. Construct a 95% two-sided CI on the mean difference in overall distance for the two brands of golf balls.
d. What is the power of the statistical test in part (b) to detect a true difference in mean overall distance of 5 yards?
e. What sample size would be required to detect a true difference in mean overall distance of 3 yards with power of approximately 0.75?