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6. 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 distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. 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 a = 0.05. What is the P-value? c. Construct a 95% two-sided Cl 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?

6. 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 distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. 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 a = 0.05. What is the P-value? c. Construct a 95% two-sided Cl 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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 25PPS
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6. 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 distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. 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 a = 0.05. What is the P-value? c. Construct a 95% two-sided Cl 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?
Transcribed Image Text:6. 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 distance hit by the legendary champion Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. 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 a = 0.05. What is the P-value? c. Construct a 95% two-sided Cl 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?
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