The American Society for Quality ASQ conducted a salary surv

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,

Solution

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.