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The PGA Players Championship was held at the Sedgefield Country Club in Greensboro, North Carolina, August 11–17, 2008. Shown here are first-round and second-round scores for a random sample of 11 golfers. Use α = .05 to determine whether the first- and second-round median scores for golfers in the Players Championship differed significantly. What is your conclusion? Golfer 1st Round 2nd Round Marvin Laird 63 74 Jimmy Walker 70 73 Kevin Chappell 72 70 Kevin Duke 65 71 Andrew Buckle 70 74 Paul Claxton 69 73 Larry Mize 72 71 Chris Riley 68 70 Bubba Watson 70 68 Carlos Franco 71 71 Richard Johnson 72 69

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Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323

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Section
BuyFindarrow_forward

Statistics for Business & Economic...

12th Edition
David R. Anderson + 4 others
Publisher: South-Western College Pub
ISBN: 9781285846323
Chapter 18.2, Problem 16E
Textbook Problem
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The PGA Players Championship was held at the Sedgefield Country Club in Greensboro, North Carolina, August 11–17, 2008. Shown here are first-round and second-round scores for a random sample of 11 golfers. Use α = .05 to determine whether the first- and second-round median scores for golfers in the Players Championship differed significantly. What is your conclusion?

Golfer 1st Round 2nd Round
Marvin Laird 63 74
Jimmy Walker 70 73
Kevin Chappell 72 70
Kevin Duke 65 71
Andrew Buckle 70 74
Paul Claxton 69 73
Larry Mize 72 71
Chris Riley 68 70
Bubba Watson 70 68
Carlos Franco 71 71
Richard Johnson 72 69

To determine

Check whether the first and second-round median scores for golfers in the Players Championship differed significantly and draw conclusion.

Explanation of Solution

Calculation:

The table summarizes the first and second round scores for the golfers. The level of significance is 0.05.

The hypotheses are given below:

Null hypothesis:

H0:Medianscore for Round 1Median score for Round 2=0

That is, there is no significant difference in the first and second-round median scores for golfers.

Alternative hypothesis:

HaMedianscore for Round 1Median score for Round 20

That is, there is significant difference in the first and second-round median scores for golfers.

The signed ranks for the golfers can be obtained as follows:

GolferRoundAbsoluteSigned Ranks
12DifferenceDifferenceRankNegativePositive
Marvin Laird6374–111110–10 
Jimmy Walker7073–335.5–5.5 
Kevin Chappell7270223 3
Kevin Duke6571–669–9 
Andrew Buckle7074–447.5–7.5 
Paul Claxton6973–447.5–7.5 
Larry Mize7271111 1
Chris Riley6870–223–3 
Bubba Watson7068223 3
Carlos Franco717100   
Richard Johnson7269335.5 5.5

The sum of the positive ranks can be denoted as T+. The Wilcoxon signed-rank test is conducted by using T+ as the test statistics.

Sum of the positive signed ranks is,

T+=1.5+7+3+3+3+5.5=12.5

It is known that if the sample size is greater than equal to 10, the approximation distribution of Wilcoxon signed rank test is Normal distribution.

Here, the difference for the golfer Carlos Franco is zero. Thus, the sample size becomes 10, which is equal to10. Thus, the distribution of T+ can be approximated as normal.

Mean, μT+=n(n+1)4

Substitute n=10 in mean of Wilcoxon signed-rank test and it is found that,

μT+=10(10+1)4=1104=27.5

Thus, the mean is 27

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Chapter 18 Solutions

Statistics for Business & Economics, Revised (MindTap Course List)
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