The U.S.Golf Association provides a number of services for its members.One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf.For example,they regularly test the golf balls made by the various companies that sell balls in the United States.Recently they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee.To conduct the test,the U.S.G.A.uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used.The following data reflect sample data for a random sample of balls of each brand. Given this information,what is the test statistic for testing whether the two population means are equal?
A)t = 1.115
B)t = 1.96
C)t = -4.04
D)t = -2.58

Question

The U.S.Golf Association provides a number of services for its members.One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf.For example,they regularly test the golf balls made by the various companies that sell balls in the United States.Recently they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee.To conduct the test,the U.S.G.A.uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used.The following data reflect sample data for a random sample of balls of each brand.  Given this information,what is the test statistic for testing whether the two population means are equal?
A)t = 1.115 
B)t = 1.96 
C)t = -4.04 
D)t = -2.58

Quizplus · Accepted Answer

From the given information, we can calculate the pooled standard deviation as 0.277. Then, using the formula for a two-sample t-test, we can calculate the test statistic as: t = (126.1 - 120.4) / (0.277 * sqrt(14/2)) = 4.04 (rounded to two decimal places). Since we are testing whether the means are different and not specifying a direction, we use a two-tailed test. Looking at a t-distribution table with 12 degrees of freedom (14-2), we can see that the critical value for a 0.05 level of significance is approximately 2.18. Since our calculated t-value (4.04) is greater than the critical value, we reject the null hypothesis that the means are equal. Therefore, the correct answer is C.

The USGolf Association Provides a Number of Services for Its Members