If 2 denotes the variance of the population of all outside diameters that would be produced by

If σ2 denotes the variance of the population of all outside diameters that would be produced by the new machine:
(1) Test H0: σ2 = .0005 versus Ha: σ2 < .0005 by setting α equal to .05.
(2) Find 95 percent confidence intervals for σ2 and σ.
(3) Using the upper end of the 95 percent confidence interval for σ, and assuming μ = 3, determine whether 99.73 percent of the outside diameters produced by the new machine are within the specification limits.
Consider an engine parts supplier and suppose the supplier has determined that the mean and the variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 3 inches and .0005. To reduce this variance, a new machine is designed, and a random sample of n = 25 outside diameters produced by this new machine has a mean of 3 inches, a variance of .00014, and a bell- shaped and symmetrical histogram.