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Average salary of blue-collar workers

While negotiating a labor contract, the president of a company argues that the mean annual earnings of blue-collar workers is less than $56,000. The labor union argues that the salary is more than $56,000. A random sample of the annual earnings of 350 blue-collar workers is taken and contained in the file LaborDispute.xls.

a. Assume the population standard deviation is $22,000 and use it to test the following hypothesis at a .01 level of significance:

H0: μ ≤ $56,000
Ha: μ > $56,000

Do the test results support the company president or the union?

b. Repeat the above hypothesis test. However, this time use the sample standard deviation in place of the population standard deviation.

c. Does replacing the population standard deviation with the sample standard deviation affect the outcome of the hypothesis test?


Solution Preview

a) Here we have:

Sample Size (n) 350
Sample Mean 58596.0981
Sample SD 16595.2246

Sample size (n) = 350, sample mean (x) = 58596.0981 and sample standard deviation (s) = 16595.2246 and population standard deviation (σ) = 22000

Null Hypothesis (Ho): µ < 56000
Alternative Hypothesis (Ho): µ > 56000 (It is one tailed, upper tailed test)
Level of Significance = 0.01
Upper Critical value is +2.33 (It is given in the standard normal table)

Decision Rule:
Reject Ho, if ...

Solution Summary

This solution is comprised of a detailed explanation of testing of one sample mean using z test. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of testing of one sample mean using z test. Null and Alternative hypotheses are defined followed by calculation of test statistics anc concluding remarks for the sub parts.