A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. Let μ denote the mean arsenic content for copper treated by this process, and assume that the standard deviation of arsenic content is σ = 100 ppm. The sample mean arsenic content X̅ of 75 copper specimens will be computed, and the null hypothesis H₀ : ≥ 1000 will be tested against the alternate H₁ :μ < 1000.

a. A decision is made to reject H₀ if X̅ ≤ 980. Find the level of this test.

b. Find the power of the test in part (a) if the true mean content is 965 ppm.

c. For what values of X̅ should H₀ be rejected so that the power of the test will be 0.95 when the true mean content is 965?

d. For what values of X̅ should H₀ be rejected so that the level of the test will be 5%?

e. What is the power of a 5% level test if the true mean content is 965 ppm?

f. How large a sample is needed so that a 5% level test has power 0.95 when the true mean content is 965 ppm?