a hypothesis test based on the scenario below and fill out the questions with your answers and statistics.

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.

You will only use one of the following numeric hypotheses and should match your narrative hypotheses: found in image 1

Note: Use the following notations for your population values: m₁ are the old golf balls and m₂ are the new ones. Add more spaces between the questions but do not change the numbers.

1.List the hypotheses for the tests:

Numeric hypotheses

a.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.

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