Exercise 2 (McClave): Par, Inc. Rev: Oct 10, 2011 Prior to doing this exercise it is strongly advised prior to doing this exercise read Chapter 7 (especially section 7.2) and: • FAQ: Lesson 11: When to use Z and t plus sigma unknown(Located in FAQ Conference AND Here as an attached file). • FAQ: Lesson 7: Test for independence. • FAQ : Lesson 4: Statistical inference and hypothesis testing • FAQ: Lesson 14: Independent Sampling versus paired/matched (dependent) • Review: Module 4! Use the attached Excel file to do the analysis but you will submit in the assignment area a Word document which is your management report to the CEO (me in this case) and the Excel file with your calculations. Your Word file should be a well-?written analysis of the questions below. Do label your headings as follows: Answer 1: “Your answer to question1” Answer 2: “Your answer to question2” Answer 3: “Your answer to question3” Answer 4: “Your answer to question4” Answer 5: “Your answer to question5” In each of the above headings you will answer the corresponding question # below. Please use this format to avoid losing points on the assignment by not labeling as shown above. In this exercise you will not need the numeric and graphic statistics except specified in the instructions. From my experience, you should be able to do the assignment in two pages or less but a paragraph will probably be insufficient. Background Par, Inc., manufactures golf equipment. Management believes that Par’s market share could be increased with the introduction of a cut-?resistant, longer-?lasting golf ball. Therefore, the research group at Par investigates a new golf ball coating designed to resist cuts and provide a more durable ball. The tests with the coating show promising results. One of the researchers, Bill voiced concern about the effect of the new coating on driving distances. Par would like the new cut-?resistant ball to offer driving distances comparable to those of the current-?model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and the current models were subjected to distance tests. 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 design. The results of the tests, with distances measured to the nearest yard, follow. These data are available in the data set Golf. Note: Assume the two population standard deviations are equal but are not known. Also assume you are dealing with two separate populations. Assignment Questions (Managerial Report): 1. Formulate and present the rationale for a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. 2. The CEO tells you (in contrast to what Bill said) that he would like to sell the new ball unless there is overwhelming evidence that the cut-?resistant ball is slower than the old ball so you should frame Rev: Oct 10, 2011 your hypothesis accordingly. Hint: you are more willing to make a Type II error (see pp. 346-?348): Analyze the data to provide the hypothesis testing conclusion and statements (at .05). You must include the z or t reject value for .05 as well as the actual computed z which is the basis for reject Ho or failure to reject Ho. You must also clearly state if you reject Ho or fail to reject the null hypothesis. Failure to do this clearly can hurt your grade. Use one of the formats hypothesis formats or the appropriate format from your textbook (can use H1 and H2). Use the following notations for your population values: µ1 are the old golf balls and µ2 are the new ones. 3. HO : µ ? µOH a : µ < µO H O : µ ? µO HO : µ = µO H a : µ > µO Ha : µ ? µO HO : µ1 ? µ2 ? 0 HO : µ1 ? µ2 ? 0 HO :µ1-µ2 =0Ha : µ1 ? µ2 > 0 H : µ ? µ < 0 H : µ ? µ ? 0 a12a12 Also include narrative versions of what ever of the above forms you use such as: Ho: The mean is … What is the p-?value for your test? What is your recommendation for Par, Inc.? 4. Provide the following descriptive summaries of the data for each model: ONLY the means and variances and the z values. 5. What is the 95% confidence interval for the difference between the means of the two populations? 6. Do you see a need for larger sample sizes and more testing with the golf balls? Discuss. Hints on improving your assignment: As was mentioned throughout the course, you are using statistics as a communications tool and need to bring in the highlights of your results into the body of your report. Include the appropriate graphical and tabular methods and bring in some of the important data in your report. Keep your Excel for the raw data and calculations. DO NOT state your conclusions without backing up with summaries and graphical methods in your narrative Word document-?-?management will not like it if you don’t! Remember this is a communications and management document. Do not copy and paste your Excel spreadsheet in the Word document! You will lose points if you say you “accept Ho” or even imply by your conclusions that you “accept the null hypothesis.” Readability for the consumer of your output is important. For example, do you need to show the reader that the mean is 1731209587.9227228292 or another mean is 57.3893333333? How does this add to understanding and doesn’t it hurt it? In the above example 1,731,209,587 (and in some cases 1.73 million) and 57.39 would be sufficient. Rev: Oct 10, 2011 I strongly urge you to draw out the distribution curve, especially during hypothesis testing, and then you will be less likely to make a mistake. This advice is continually ignored and therefore I see many students making mistakes not only on this assignment but on exams. You do not however, need to include it in your submission. Again, if you fail to reject Ho it doesn’t mean you accept it! This is conceptually wrong! You should always say you fail to reject. If you don’t understand why you don’t accept Ho (you can accept Ha) then post in Q & A and we can discuss. Note: If you do not understand the task please email me with your question but state in your email that you did read the assignments listed at the top of this page or I will assume you have not and will refer you back to the readings.