Question

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?

a. Use α = .10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. What is the p-value? What is your conclusion?

Answer 1

To determine if the mean score for the first round of a PGA Tour event is significantly different from the mean score for the fourth and final round, we can conduct a hypothesis test using a paired t-test.

Step-by-step explanation:

To test if the mean score for the first round of a PGA Tour event is significantly different from the mean score for the fourth and final round, we can conduct a hypothesis test. Let's use α = .10 as the significance level.

The null hypothesis (H0) is that there is no significant difference between the population means for the first and fourth rounds of scores. The alternative hypothesis (HA) is that there is a significant difference between the population means.

We can use a paired t-test to compare the means of the first and fourth round scores. We calculate the t-test value and the p-value. The p-value tells us the likelihood of observing the data if the null hypothesis is true.

If the p-value is less than α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.