Objective 15g Formulate hypothesis tests involving samples from two populations regarding population variances. And Objective 8e Calculate probabilities using F-distributions.

The piston diameter of a certain pump is supposed to be 0.4 inch. The manager of the factory collected a simple random sample of 64 pistons and measured the diameter, finding that those diameters were normally distributed, with a mean of 0.40 inch and a standard deviation of 0.0034 inch. After recalibrating the production machine, the manager randomly selects 25 pistons and determines that the mean is still 0.40 inches but the standard deviation is 0.0022 inch. The manager claims that the standard deviation has decreased significantly. Test this claim at the =0.10 level of significance. Use the P-value method.