Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table (Golfweek, February 14, 2009, and February 28, 2009). Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down? Player First Round Final Round Sleve McDichael 72 72 Onson Sweemey 68 68 Darryl Archideld 72 72 Anatoli Smorin 68 68 Rey McScriff 73 73 Glenallen Mixon 69 69 Mario McRlwain 74 74 Raul Chamgerlain 69 73 Mike Sernandez 70 73 Tony Smehrik 71 69 Player First Round Final Round Bobson Dugnutt 73 75 Willie Dustice 65 73 Scott Dourque 68 70 Shown Furcotte 70 68 Dean Wesrey 69 76 Mike Truk 72 72 Dwigt Rortugal 70 77 Tim Sandaele 72 66 Karl Dandleton 69 70 Todd Bonzalez 69 69 2b. What is the point estimate of the difference between the two population means? For which round is the population mean score lower?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table (Golfweek, February 14, 2009, and February 28, 2009). Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?



Player	First Round	Final Round
Sleve McDichael	72	72
Onson Sweemey	68	68
Darryl Archideld	72	72
Anatoli Smorin	68	68
Rey McScriff	73	73
Glenallen Mixon	69	69
Mario McRlwain	74	74
Raul Chamgerlain	69	73
Mike Sernandez	70	73
Tony Smehrik	71	69
Player	First Round	Final Round
Bobson Dugnutt	73	75
Willie Dustice	65	73
Scott Dourque	68	70
Shown Furcotte	70	68
Dean Wesrey	69	76
Mike Truk	72	72
Dwigt Rortugal	70	77
Tim Sandaele	72	66
Karl Dandleton	69	70
Todd Bonzalez	69	69

2b. What is the point estimate of the difference between the two population means? For which round is the population mean score lower?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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