The American Society for Quality (ASQ) conducted a salary survey of all its memb
ID: 3428548 • Letter: T
Question
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:
Data extracted from J. Seaman and I. Allen,
Job Title Sample Size Mean Standard Deviation Master Black Belt 86 113,276 26,466 Green Belt 15 75,917 29,000Explanation / 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
DF = 15-1 =14
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p value for two tailed = 0.00
Reject null hypothesis.
Conclusion: The two sample means are statistically significant.
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b) t test for comparing two sample means with unequal variances is the best suited here.
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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.
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The conclusion that the mean salary of master black belts greater than the mean salary of green belts holds good.
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 Mean diff 37,359 std error 47.340020272 t statistic 789.1631602Related Questions
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