question archive The American Society for Quality (ASQ) conducted a salary survey of all its members
The American Society for Quality (ASQ) conducted a salary survey of all its members
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The American Society for Quality (ASQ) conducted a 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,
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Answer:
The question is about comparing two sample means using t test.
Let x represent the Masterblack belt and y Green belt.
H0: xbar = y bar
Ha: xbar not equals y bar
| Job Title | Sample Size | Mean | Standard Deviation | variancess^2/n | ||
| x | Master Black Belt | 86 | 113,276 | 26,466 | 307.744186 | |
| y | Green Belt | 15 | 75,917 | 29,000 | 1933.333333 | |
| Total | 101 | 2241.077519 | ||||
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||||||
| Mean diff | 37,359 | |||||
| std error | 47.340020272 | |||||
| t statistic | 789.1631602 | |||||
DF = 15-1 =14
p value for two tailed = 0.00
Reject null hypothesis.
Conclusion: The two sample means are statistically significant.
b) t test for comparing two sample means with unequal variances is the best suited here.
c) Set hypotheses like this shown below and use right tailed test.
H0: xbar = y bar
Ha: xbar > y bar
t value = 789.16 ( the same as above)
p value for right tailed = 0.00001
As p value <0.05, reject null hypothesis.
The conclusion that the mean salary of master black belts greater than the mean salary of green belts holds good.
