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 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 insurance claim 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=0.05=0.05is used?