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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.

**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:*

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

*Alternative hypothesis:*

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:

Golfer | Round | Absolute | Signed Ranks | ||||

1 | 2 | Difference | Difference | Rank | Negative | Positive | |

Marvin Laird | 63 | 74 | –11 | 11 | 10 | –10 | |

Jimmy Walker | 70 | 73 | –3 | 3 | 5.5 | –5.5 | |

Kevin Chappell | 72 | 70 | 2 | 2 | 3 | 3 | |

Kevin Duke | 65 | 71 | –6 | 6 | 9 | –9 | |

Andrew Buckle | 70 | 74 | –4 | 4 | 7.5 | –7.5 | |

Paul Claxton | 69 | 73 | –4 | 4 | 7.5 | –7.5 | |

Larry Mize | 72 | 71 | 1 | 1 | 1 | 1 | |

Chris Riley | 68 | 70 | –2 | 2 | 3 | –3 | |

Bubba Watson | 70 | 68 | 2 | 2 | 3 | 3 | |

Carlos Franco | 71 | 71 | 0 | 0 | |||

Richard Johnson | 72 | 69 | 3 | 3 | 5.5 | 5.5 |

The sum of the positive ranks can be denoted as

Sum of the positive signed ranks is,

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

Mean,

Substitute

Thus, the mean is 27

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

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