What is power? You manufacture and sell a liquid product whose electrical conductivity is supposed to be 5. You plan to make six measurements of the conductivity of each lot of product. If the product meets specifications, the mean of many measurements will be 5. You will therefore test H0 : m = 5 Ha : m ≠ 5 If the true conductivity is 5.1, the liquid is not suitable for its intended use. You learn that the power of your test at the 5% significance level against the alternative m = 5.1 is 0.23.

(a) Explain in simple language what “power = 0.23”

means in this setting.

(b) You could get higher power against the same alternative with the same a by changing the number of measurements you make. Should you make more measurements or fewer to increase power?

(c) If you decide to use a = 0.10 in place of a = 0.05, with no other changes in the test, will the power increase or decrease? Justify your answer.

(d) If you shift your interest to the alternative m = 5.2, with no other changes, will the power increase or decrease? Justify your answer