a manufacturer of golf equipment and has developed a new golf ball that has been
ID: 2946272 • Letter: A
Question
a manufacturer of golf equipment and has developed a new golf ball that has been provide "extra distance". In a test of driving distance using a mechanical driving 5. Par, Inc. is designed to device, a Ltd., a competitor. The sample data is below. sample of Par golf balls was compared with a sample of golf balls made by Rap, Sample 1 Sample2 80 balls Sample size Sample mean Sample standard deviation 120 balls 235 yards 15 yards 218 yards 20 yards Can we conclude, using a 0.01 level of significance, that the mean driving distance of Par, Inc. golf balls is greater than the mean driving distance of Rap, Ltd. Golf balls?Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1< u2
Alternative hypothesis: u1 > u2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample z-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), and the z statistic test statistic (z).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 2.622
z = [ (x1 - x2) - d ] / SE
z = 6.48
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a z statistic of 6.48
Therefore, the P-value in this analysis is less than 0.0001.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that mean driviing distance of Par inc golf balls is greater than the mean driving distance of Rap ltd. golf balls.
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