You manufacture and sell a liquid produce whose electrical conductivity is supposed to be 5. You plan to make 10 measurements of the conductivity of each lot of product. You know that the population standard deviation of your measurements is 2. You want to test whether the liquid produced meet the target conductivity, on average.

(a) Suppose the 6 measurements are 5.2, 4.9, 5, 5, 4.8, 5, 4.5, 5.1, 4.7, 4.9. Find the value of the test statistic

(b)  If I use a sample of size 20 and use the same testing rule, will the power increase or decrease?

(c) Suppose I used an arbitrary testing rule that has 80% power when myu=4.9. Explain in simple language what that means