A Better Golf Tee? An independent golf equipment testing...

A Better Golf Tee? An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular $2-3 / 4^{\prime \prime}$ wooden tee to those hit off a $3^{\prime \prime}$ 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 total distance traveled (in yards) with each type of tee, based on the test results, are provided on the WeissStats CD. a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. At the $1 \%$ significance level, do the data provide sufficient evidence to conclude that, on average, the Stinger tee improves total distance traveled? c. Find a $99 \%$ confidence interval for the difference between the mean total distance traveled with the regular and Stinger tees. d. Are your procedures in parts (b) and (c) justificd? Why or why not?

A Better Golf Tee? An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a regular $2-3 / 4^{\prime \prime}$ wooden tee to those hit off a
$3^{\prime \prime}$ 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 total distance traveled (in yards) with each type of tee, based on the test results, are provided on the WeissStats CD.
a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples.
b. At the $1 \%$ significance level, do the data provide sufficient evidence to conclude that, on average, the Stinger tee improves total distance traveled?
c. Find a $99 \%$ confidence interval for the difference between the mean total distance traveled with the regular and Stinger tees.
d. Are your procedures in parts (b) and (c) justificd? Why or why not?

Key Concepts

Assumptions in Parametric Procedures

Conducting hypothesis tests and constructing confidence intervals using methods such as the t-test requires certain assumptions to be met, including the normality of the data, independence of observations, and, in some cases, equality of variances. Assessing these assumptions through preliminary data analysis (using graphical methods or summary statistics) is crucial for the validity of the inferential procedures.

Confidence Intervals for Mean Differences

A confidence interval for the difference between two means provides a range of plausible values for this difference with a certain degree of confidence. It quantifies uncertainty in the estimate using the variability observed in the sample data and is particularly useful in understanding the magnitude and practical significance of the difference.

Graphical Data Analysis

This concept involves using visual tools like normal probability plots and boxplots to examine the distribution of data. These plots help determine if the data follow a normal distribution, identify any outliers, and understand the spread and symmetry of the data, which are all fundamental steps in assessing whether parametric methods are appropriate.

Two-Sample Hypothesis Testing

This refers to the statistical method used to compare the means of two independent samples. By setting up null and alternative hypotheses, one can use a test statistic (typically a t-statistic when variances are unknown) to determine, at a specified significance level, whether there is sufficient evidence to conclude a difference in means between the groups under study.

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