SOLUTION: As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000. The union would like to show the mean is lower. A random sample o

Question 314594: As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000. The union would like to show the mean is lower. A random sample of 17 annual clerical salaries is collected and yields a sample mean of $28,157 and standard deviation of $3500. Is this sufficient evidence to support the Union's position? Use a significance level of a = 0.05. You may assume the mean annual salaries are normally distributed.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000.
The union would like to show the mean is lower.
Ho: u = 30,000
Ha: u < 30,000
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A random sample of 17 annual clerical salaries is collected and yields a sample mean of $28,157 and standard deviation of $3500. Is this sufficient evidence to support the Union's position? Use a significance level of a = 0.05. You may assume the mean annual salaries are normally distributed.
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t(28157) = (28157-30000)/[3500/sqrt(17)] = -2.1711
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p-value: P(t<-2.1711 with df = 16) = 0.0227
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Conclusion: Since the p-value is less than 5%, reject
Ho. The test results do not support mgmt's opinion.
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Cheers,
stan H.
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