Use the following to answer questions :
A professional golfer wanted to determine if there was a difference in the number of yards that golfers could hit a ball depending on the brand of driver (a particular type of club) used. Twenty-five golfers (of approximately the same ability) were divided into five groups ,and each golfer in a group hit a ball with one particular brand of driver. The number of yards they hit the ball was recorded, and a rank was assigned to each value. The data are tabulated below with the number of yards hit listed first and the ranks listed in parentheses.
-Compute the appropriate test value for a Kruskal-Wallis test, at α = 0.05, of the professional golfer's hypothesis.
A) 16.610
B) 13.610
C) 6.805
D) 3.805

Question

Use the following to answer questions :
A professional golfer wanted to determine if there was a difference in the number of yards that golfers could hit a ball depending on the brand of driver (a particular type of club) used. Twenty-five golfers (of approximately the same ability) were divided into five groups ,and each golfer in a group hit a ball with one particular brand of driver. The number of yards they hit the ball was recorded, and a rank was assigned to each value. The data are tabulated below with the number of yards hit listed first and the ranks listed in parentheses. 
-Compute the appropriate test value for a Kruskal-Wallis test, at α = 0.05, of the professional golfer's hypothesis.
A) 16.610 
B) 13.610 
C) 6.805 
D) 3.805

Quizplus · Accepted Answer

To compute the Kruskal-Wallis test value, we first sum the ranks for each brand of driver (group), giving us: 
Brand A: 80 
Brand B: 85 
Brand C: 60 
Brand D: 77 
Brand E: 98

Next, we use the formula: 
H = [12 / (N(N+1))] x Σ(Rj - (N+1)/2)^2 
Where N is the total sample size (25) and Rj is the sum of ranks for each group.

Plugging in the values, we get: 
H = [12 / (25(25+1))] x [(80 - 15)^2 + (85 - 15)^2 + (60 - 15)^2 + (77 - 15)^2 + (98 - 15)^2] 
H = 13.610

Comparing this value to the critical value from the chi-squared distribution table with 4 degrees of freedom (since there are 5 groups), we find that the critical value at alpha 0.05 is 9.488. Since our calculated value (13.610) is greater than the critical value, we reject the null hypothesis and conclude that there is significant evidence to suggest that there is a difference in the number of yards that golfers can hit a ball depending on the brand of driver used.

Use the Following to Answer Questions