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# statistics on excel

Golf Equipment, Inc. has developed a new coating designed to resist cuts and provide a more durable golf ball. One concern for Golf Equipment was the effect of the new coating on driving distances. Some board members were hypothesizing that the mean driving distance of the new golf ball will either be longer or shorter than the mean driving distance of the current golf ball. This would seriously question the future production of the new ball because of the USGA strict recommendations and golfers expectations. Therefore, Gold Equipment would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the mean driving distances for the two balls, 40 balls of both new and current models were subjected to distance test. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. The sample data (in yards) is available in the attached Excel file.

1. Provide descriptive statistical summaries of the data for each model. What are your primary observations concerning the two data sets? Calculate the 95% confidence interval for the population mean of each model.

2. Formulate a hypothesis test for the comparison of the mean driving distances of the current and new golf balls.

3. Analyze data to provide a hypothesis testing conclusion.

4. Calculate the 95% confidence interval for the difference between the means of the two populations. What can be concluded from this interval?

5. What is your final recommendation concerning the production of the new balls?

**Instructions**

1. To complete Task 1, apply “Descriptive Statistics” in Data Analysis of Excel (see instructions on pages 377-378). In the row “Confidence Level (95.0%)” of the Descriptive Statistics printout you will see the margin of error of the confidence interval for the corresponding population mean. You may watch the relevant video: www.youtube.com/watch?v=EvVi_S5ZbMI

2. To complete Task 2, formulate the null and alternative hypotheses, define clearly the used symbols, and present the rationale for your hypotheses.

3. To complete Task 3, apply “t-Test; Two-sample Assuming Unequal Variances” in Data Analysis of Excel (see instructions on page 479). Assume α = 0.05. Note: You may watch a video about this test at:www.youtube.com/watch?v=nVWPc-mPbOU

4. You cannot find by Excel the 95% confidence interval for the difference between the means of the two populations. Therefore, to complete Task 4, you should apply formula (10.6) by hand. However, in Excel’s output from “t-Test; Two-sample Assuming Unequal Variances”, you can find the degrees of freedom computed using formula (10.7) as well as the needed critical value tα/2.

Use Microsoft Word to write a managerial report in which you include your answers to all four tasks, and summarize your findings. Your report should also include all your Excel outputs (copy and paste them), so do not attach any separate Excel files. **Hint**. You may assume that you are working for Golf Equipment, Inc. and your boss, who has a very limited knowledge about business statistics, asked you to conduct a statistical analysis concerning the comparison of performance of the current golf ball and the golf ball with the new coating. You report may look like a letter written to your boss in which you present your findings and make recommendation on the production of the new golf ball.