Question

The X-Factor in golf performance. Many golf teaching professionals believe that a greater hip-to-shoulder differential angle during the early downswing - dubbed the "X-Factor"-leads to improved golf performance. The Journal of Quantitative Analysis in Sports (Vol. 5, 2009) published an article on the X-Factor and its relationship to golfing performance. The study involved 15 male golfers with a player handicap of 20 strokes or less. The golfers were divided into two groups: 8 golfers with a handicap of 10 strokes or less (low-handicapped group) and 7 golfers with a handicap between 12 and 20 strokes (highhandicapped group). The X-Factor, i.e., the hip-to-shoulder differential angle (in degrees), was measured for each golfer at the top of the backswing during his tee shot. The researchers hypothesized that low-handicapped golfers will tend to have higher X-factors than high-handicapped golfers. The researchers also discovered that the sample data were not normally distributed. Consequently, they applied a nonparametric test. a. What nonparametric test is appropriate for analyzing these data? b. Specify the null and alternative hypotheses of interest in the words of the problem. c. Give the rejection region for this test, using α=.05. d. The researchers reported a p-value of .487. Use this result to draw a conclusion.

Answer 1

A suitable nonparametric test for the X-Factor study is the Mann-Whitney U test. The null hypothesis claims no significant difference in X-Factor between two handicap groups, which is not rejected due to a p-value of 0.487, indicating no statistical evidence of a difference.

Step-by-step explanation:

The appropriate nonparametric test for analyzing the X-Factor data involving the hip-to-shoulder differential angle among golfers with different handicaps is likely the Mann-Whitney U test since the data are not normally distributed and are from independent samples.

Hypothesis Definition

• Null Hypothesis (H0): There is no significant difference in the X-Factor between low-handicapped and high-handicapped golfers.
• Alternative Hypothesis (Ha): Low-handicapped golfers have a significantly higher X-Factor than high-handicapped golfers.

Rejection Region

For a nonparametric test with α = 0.05, the rejection region comprises outcomes where the test statistic falls in the extreme 5% of its distribution.

Conclusion of the Study

Given the reported p-value of 0.487, we do not reject the null hypothesis as it is greater than the significance level of 0.05. This suggests that there is not enough statistical evidence to conclude that low-handicapped golfers have a significantly higher X-Factor than high-handicapped golfers in this sample.