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     2a. Use α=0.10 to test for a statistically significant difference between the population means for first- and fourth-round scores. What is the p-value? What is your conclusion?

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 + ...