Question

An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular \(2-3/4"\) wooden tee to those hit off a \(3"\) Stinger Competition golf 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. Data on ball velocity (in miles per hour) with each type of tee based on the test results are provided on Th WeiessStats site. Use the technology of your choice to do the following.

a. Obtain normal probability plots, boxplots and the standard deviation for the two samples.

b. Bases on your results from part (a) which would you be inclined to use to compare the population means: a pooled or a nonpooled \(t-\)procedure? Explain your answer.

c. At the \(5%\) significance level, do the data provide sufficient evidence to conclude that on average ball velocity is less with the regular tee than with the Stinger tee? Perform the required hypothesis test by using both the pooled \(t-\)test and the nonpooled \(t-\)test and compare results.

d. Find a \(90%\) confidence interval for the difference between the mean ball velocities with the regular and Stinger tees. Obtain the reuiqred confidence interval by using both the poold \(t-\)interval procedure and the nonpooled \(t-\)interval procedure. Compare your results.

Short answer

Part a.

Part b. From the summary statistics of two samples, the pooled test is in appropriate because samples are considerably different.

Part c. The \(P(0.000)\leq (\alpha =0.05)\) so, the null hypothesis is rejected.

Part d. See Explanation

Step-by-step solution

Part a. Step 1. Given information

Consider the data,

Part a. Step 2. Calculation

The normal probability curve is,

And

The box plot is,

And

Part b. Step 1. Explanation

From the summary statistics of two samples, the pooled test is in appropriate because samples are considerably different.

Part c. Step 1. Calculation

For non pooled test,

The \(P(0.000)\leq (\alpha =0.05)\) so, the null hypothesis is rejected.

And for pooled,

The \(P(0.000)\leq (\alpha =0.05)\) so, the null hypothesis is rejected.

Part d. Step 1. Explanation

For non pooled test,

And for pooled test,