The American Society for Quality (ASQ) conducted the salary survey of all its members. ASQ members work in all areas of manufacturing and service-related institutions, with a common theme of an interest in quality. Two job titles are master black belt and green belt. (See Section 14.6, for a description of these titles in a Six Sigma quality improvement initiative.) Descriptive statistics concerning salaries for these two job titles are given in the following table:
| Job Title |
Sample Size |
Mean |
Standard Deviation |
| Master Black Belt |
86 |
113,276 |
26,466 |
| Green Belt |
15 |
75,917 |
29,000 |
Data extracted from J. Seaman and I. Allen, "Revealing Answers," Quality Progress, December 2010, p. 31.
a. Using a 0.05 level of significance, is there a difference in the variability of salaries between master black belts and green belts?
b. Based on the result of (a), which t test defined in Section 10.1 is appropriate for comparing mean salaries?
c. Using a 0.05 level of significance, is the mean salary of master black belts greater than the mean salary of green belts?