The union negotiations between labor and management at the Stone Container paper mill in Minnesota hit a snag when management asked labor to take a cut in health insurance coverage. As part of its justification, management claimed that the average amount of insurance claims filed by union employees did not exceed $250 per employee. The union’s chief negotiator requested that a sample of 100 employees’ records be selected and that this claim be tested statistically. The claim would be accepted if the sample data did not strongly suggest otherwise. The significance level for the test was set at 0.10.
a. State the null and alternative hypotheses.
b. Before the sample was selected, the negotiator was interested in knowing the power of the test if the mean amount of insurance claims was $260. (Assume the standard deviation in claims is $70.00, as determined in a similar study at another plant location.) Calculate this probability for the negotiator.
c. Referring to part b, how would the power of the test change if α = 0.05 is used?
d. Suppose alpha is left at 0.10, but the standard deviation of the population is $50.00 rather than $70.00. What will be the power of the test? State the generalization that explains the relationship between the answers to part b and d.
e. Referring to part d, based on the probability computed, if you were the negotiator, would you be satisfied with the sampling plan in this situation? Explain why or why not. What steps could be taken to improve the sampling plan?