8. (21 Pts) An independent golf equipment testing facility compared the differen

Question

8. (21 Pts) An independent golf equipment testing facility compared the difference in the perfe of golf balls hit off a regular 2-3/4 inch wooden tee to those hit off a 3 inch Stine tee. A Callaway Great Big Bertha driver with 10 degrees of loft was used for the test and a robot swung the club head at approximately 95 miles per hour. A random sample of 30 for each tee type and the ball velocity (mph) was recorded. At a 5% significance level provide sufficient evidence to claim, that, on average, ball velocity is less with the regular tee than with the Stinger tee. NOTE: NO COMPUTATIONS ARE REQUIRED. i. This problem is about (circle the correct one): One population mean Two population means, independent samples Two population means, paired samples One population standard deviation State the null and alternate hypotheses. iii. What is the level of significance? iv. List the assumptions and show the numbers or information given to meet each assumption. The P-value for normality test is 0.4001 for regular tee and 0.5087 for Stinger tee. v. Circle which of the following Statcrunch methods you would use to test the hypothesis state in part (b). z Stats - One sample I Stats - One sample T Stats - Two samples I Stats – Paired Sample Variance tests – One sample None of these since not all assumptions are met vi. If the P-value is

Explanation / Answer

1) Two population independet samples

2) Null:Ball velocity regular tee than with Stinger Tee

Alt: Ball velocity is less with regular tee than with Stinger Tee

3) Level = 0.05

4) Assumption:

Distribution is normal

Since, sample size is = 30, it can be assumed that sample is normal

The test rejects the hypothesis of normality when the p-value is less than or equal to 0.05. Failing the normality test allows you to state with 95% confidence the data does not fit the normal distribution. Passing the normality test only allows you to state no significant departure from normality was found.

As both p values > 0.05, both data are normal

5) T test two samples

6) In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist.

Here, p < 0.05

Thus null is rejected

7) As null is rejected, we can interpret that Ball velocity is less with regular tee than with Stinger Tee

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