Par For the Course Problem (you are the statistician reporting to the CEO)

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.

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 your hypothesis accordingly. Ten million dollars has already been spent on the new ball and the future of the company could be at stake.Hint: you are more willing to make a Type II error: Analyze the data to provide the hypothesis testing conclusion and statements (at .05). 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: 1 are the old golf balls and 2 are the new ones.

Note: Assume the two population standard deviations are equal but are not known. Also assume you are dealing with two separate populations.

Keep your Excel for the raw data and calculations. 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.

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. 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.

Par for the Course (answer all and submit with your Excel)

Note: Use the following notations for your population values: m₁ are the old golf balls and m₂ are the new ones. Pretend this is a management report although in the form of an answer Add more spaces between the questions but do not change the numbers.

1.List the hypotheses for the tests:

a.Numeric hypotheses

b.Narrative hypotheses (should match above but in English)

2.Before you draw the sample

a.Is it a dependent (paired) or independent sample?

b.What is the z or t value (rejection rule) you will test for at .05?

c.Why did you use z or t?

d.Based on the above what is your rejection rule for the null hypothesis? Describe in a few sentences and explain 2b to your "test statistic".

3.Post Sample statistics

a.What is the value of your test statistic (include if it is z or t)?

b.What is your actual p value?

c.What are your two means? List clearly the means for sample 1 and sample 2.

d.What is the standard deviation?

e.What is the 95% confidence interval for the difference between the means of the two populations?

4.Evaluation of your Hypotheses after you have drawn the samples

a.Test statistic method:based on the results in 3a compare the test statistic to your precomputed rejection rule in 2b and if you reject or fail to reject Ho (the null hypotheses is)?Use complete sentences, include values and clearly state "reject Ho" or "fail to reject Ho."

b.P Value method:based on the results in 3b compare the p value to your alpha leveland if you reject or fail to reject Ho (the null hypotheses is)?Use complete sentences, include values and clearly state "reject Ho" or "fail to reject Ho." You will basically get the same answer as 4b but based on a slightly different analysis.

5.Your recommendation to the CEO.Based on your analysis of the above and your discussion of the CEO what is your recommendation? State the facts and the results of your hypothesis test. Use complete sentences.

Current 264.00 261.00 267.00 272.00 258.00 283.00 258.00 266.00 259.00 270.00 263.00 264.00 284.00 263.00 260.00 283.00 255.00 272.00 266.00 268.00 270.00 287.00 289.00 280.00 272.00 275.00 265.00 260.00 278.00 275.00 281.00 274.00 273.00 263.00 275.00 267.00 279.00 274.00 276.00 262.00

New 277.00 269.00 263.00 266.00 262.00 251.00 262.00 289.00 286.00 264.00 274.00 266.00 262.00 271.00 260.00 281.00 250.00 263.00 278.00 264.00 272.00 259.00 264.00 280.00 274.00 281.00 276.00 269.00 268.00 262.00 283.00 250.00 253.00 260.00 270.00 263.00 261.00 255.00 263.00 279.00