A machine is designed to produce gaskets with a mean inside diameter of 0.375 Inch. A consultant recommended the gaskets be made with a different, more durable material. An engineer, worried that the new material might cause the mean inside diameter of the gaskets to differ from the target of 0.375, proposed using the new material for one day then selecting a random sample of 20 gaskets to determine if the mean inside diameter had changed. They will test the hypotheses
H0 : μ = 0.375
Ha : μ ≠ 0.375
a) Suppose that the population of inside diameters of this type of gasket is normally distributed with standard deviation σ = 0.005 inch. State the appropriate test statistic to test these hypotheses, and give its distribution under the null hypothesis.
b) State the rejection region for the test statistic. Use an α = 0.01 level of significance.
c) Suppose that a random sample of n = 20 gaskets had a mean of 0.373 inches. Calculate the value of the test statistic.
d) Make a decision as to whether or not to reject the null hypothesis, and state a conclusion in plain English (using complete sentences).