Question

Par, inc. is a manufacturer of golf equipment and has developed a new golf ball that has been designed to provide ‘extra distance.” In a test if driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor (given in the table below). Also, based on the data from previous driving distance tests, the two population standard deviations are known with s₁= 15 yards and s₂= 20 yards. (Research Quantitative Marketing) (Inferential Analysis and Hypothesis Testing)

Sample 1: Par Inc. Sample 2: Rap Ltd.

Sample size: 120 balls 80 balls

Sample Mean: 275 yards 258 yards

1.What is the null and alternate hypothesis? (provide your answer in words and then quantify it as shown in the slides)?

2.What is the appropriate test to use in this case?

3.What is your “observed” and “critical value” of the test statistic?

4.What is your conclusion if the level of significance (?) =10%. Use either p-value or critical value approach to come to this conclusion.

Answer 1

1. In a test if driving distance is observed for two companies we have to check whether there is an actual betterment in the new golf ball which claims that it is designed to provide extra distance. The null hypothesis should test that the sample means are equal while the alternative hypothesis will test that sample mean of Par, inc is greater than Rap, Ltd. If the null hypothesis is accepted then the alternative will be rejected and we can say that there is no difference in distance covered by each company golf ball while, if the null hypothesis is rejected then the alternative hypothesis will be accepted which means the golf ball of Par, inc provides more distance than golf ball og Rap, Ltd

H₀: Sample mean 1 = Sample mean 2

H₁: Sample mean 1 > Sample mean 2

where, H₀ is the null hypothesis and H₁ is the alternative hypothesis.

2. The most appropriate test to use in this case is t-test. t-test is used to determine whether the means of two groups are equal to each other.