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Q10E

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Statistics For Business And Economics
Found in: Page 398
Statistics For Business And Economics

Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593

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Short Answer

Play Golf America program. The Professional Golf Association (PGA) and Golf Digest have developed the Play Golf America program, in which teaching professionals at participating golf clubs provide a free 10-minute lesson to new customers. According to Golf Digest, golf facilities that participate in the program gain, on average, $2,400 in greens fees, lessons, or equipment expenditures. A teaching professional at a golf club believes that the average gain in greens fees, lessons, or equipment expenditures for participating golf facilities exceeds $2,400.

a. In order to support the claim made by the teaching professional, what null and alternative hypotheses should you test?

b. Suppose you select α = 0.05. Interpret this value in the words of the problem.

c. For α = 0.05, specify the rejection region of a large sample test.

a. The null and the alternative hypotheses are H0 : μ0 = $2400 against Ha : μ > $2400

b. Testing α at 0.05 means there is a 5% risk that the researcher will decide that the mean gains are greater than $2400 when they are not.

c. {x: Z ≥ 1.645}

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given information

Participating golf facilities receive an average of $2,400. According to a teaching professional at a golf club, the average increase in greens fees, lessons, or equipment purchases for participating in facilities exceeds $2,400.

Step 2: Specifying the null and the alternative hypothesis

a.

The null hypothesis is the assumed-true hypothesis, while the alternative hypothesis is the hypothesis that must be demonstrated with the data.

It is assumed that the mean of the gain is $2400, making it the null hypothesis. The researcher seeks to prove that the mean of the gain exceeds $2400, making it the alternative hypothesis.

i.e.

H0 : μ0 = $2400 against Ha : μ > $2400

Step 3: Interpretation

b.

In the context of hypothesis testing, α denotes the risk that will reject the null hypothesis when it is, in fact, true. In the context of this problem, in testing 0.05, there is a 5% risk that the researcher will decide that the mean gains are more significant than $2400 when they are not.

Step 4: Specifying the rejection region

c.

For large sample tests, Z distribution can be used where

Z ~ N (0,1)

Let x be the critical value

Then, P (Z > x) = 0.05

From the standard normal table,

x = 1.645

So, the critical region is

[x,∞) = [1.645,∞ )

={x: Z ≥ 1.645}

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