The increased availability of light materials with high strength has revolutionized the design and manufacture of golf clubs, particularly drivers. Clubs with hollow heads and very thin faces can result in much longer tee shots, especialy for players of modest skills. This is due partly to the "spring- like effect" that the thin face imparts to the ball. Firing a golf ball at the head of the club and measuring the ratio of the out- going velocity of the ball to the incoming velocity can quan- tify this spring-like effect. The ratio of velocities is called the coefficient of restitution of the club. An experiment was per- formed in which 15 drivers produced by a particular club maker were selected at random and their coefficients of resti- tution measured. In the experiment the golf balls were fired from an air cannon so that the incoming velocity and spin rate of the ball could be precisely controlled. It is of in- terest to determine if there is evidence (with a = 0.05) to sup- port a claim that the mean coefficient of restitution exceeds 0.82. The observations follow: 0.8411 0.8191 0.8182 0.8125 0.8750 0.8580 0.8532 0.8483 0.8276 0.7983 0.8042 0.8730 0.8282 0.8359 0.8660 In performing the appropriate hypothesis test, what is the critical value? Answer with 3 decimal places.
The increased availability of light materials with high strength has revolutionized the design and manufacture of golf clubs, particularly drivers. Clubs with hollow heads and very thin faces can result in much longer tee shots, especialy for players of modest skills. This is due partly to the "spring- like effect" that the thin face imparts to the ball. Firing a golf ball at the head of the club and measuring the ratio of the out- going velocity of the ball to the incoming velocity can quan- tify this spring-like effect. The ratio of velocities is called the coefficient of restitution of the club. An experiment was per- formed in which 15 drivers produced by a particular club maker were selected at random and their coefficients of resti- tution measured. In the experiment the golf balls were fired from an air cannon so that the incoming velocity and spin rate of the ball could be precisely controlled. It is of in- terest to determine if there is evidence (with a = 0.05) to sup- port a claim that the mean coefficient of restitution exceeds 0.82. The observations follow: 0.8411 0.8191 0.8182 0.8125 0.8750 0.8580 0.8532 0.8483 0.8276 0.7983 0.8042 0.8730 0.8282 0.8359 0.8660 In performing the appropriate hypothesis test, what is the critical value? Answer with 3 decimal places.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:The increased availability of light materials with high
strength has revolutionized the design and manufacture of
golf clubs, particularly drivers. Clubs with hollow heads and
very thin faces can result in much longer tee shots, especialy
for players of modest skills. This is due partly to the "spring-
like effect" that the thin face imparts to the ball. Firing a golf
ball at the head of the club and measuring the ratio of the out-
going velocity of the ball to the incoming velocity can quan-
tify this spring-like effect. The ratio of velocities is called the
coefficient of restitution of the club. An experiment was per-
formed in which 15 drivers produced by a particular club
maker were selected at random and their coefficients of resti-
tution measured. In the experiment the golf balls were
fired from an air cannon so that the incoming velocity and
spin rate of the ball could be precisely controlled. It is of in-
terest to determine if there is evidence (with a = 0.05) to sup-
port a claim that the mean coefficient of restitution exceeds
0.82. The observations follow:
0.8411
0.8191
0.8182
0.8125
0.8750
0.8580
0.8532
0.8483
0.8276
0.7983
0.8042
0.8730
0.8282
0.8359
0.8660
In performing the appropriate hypothesis test, what is the critical value?
Answer with 3 decimal places.
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