Consider an Engine Parts Supplier and Suppose the Supplier Has

Short Answer

Consider an engine parts supplier and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. If σ² denotes the variance of the population of all outside diameters that would be produced by the new machine, test H₀: σ² = .00075 versus H_a: σ² < .00075 by setting α = .05.