Question: Referring to Problem, suppose that there were 40 ties at eight different salary levels. The following shows how many scores were ties at each salary level:
Level t
1 2
2 3
3 2
4 4
5 8
6 10
7 6
5
a. Given the results in the previous exercise, is it necessary to use the H-value adjusted for ties?
b. If your answer to part a is yes, conduct the test of hypothesis using this adjusted value of H. If it is not, explain why not.
Problem: A study was conducted by the sports department of a national network television station in which the objective was to determine whether a difference exists between median annual salaries of National Basketball Association (NBA) players, National Football League (NFL) players, and Major League Baseball (MLB) players. The analyst in charge of the study believes that the normal distribution assumption is violated in this study. Thus, she thinks that a nonparametric test is in order. The following summary data have been collected:
NBA NFL MLB
n = 20 n = 30 n = 40
ΣRi = 1,655 ΣRi = 1,100 ΣRi = 1,340
a. Why would the sports department address the median as the parameter of interest in this analysis, as opposed to the mean? Explain your answer.
b. What characteristics of the salaries of professional athletes suggest that such data are not normally distributed? Explain.
c. Based on these data, what can be concluded about the median salaries for the three sports? Test at an = 0.05. Assume no ties.