Consider engine parts supplier and assume the supplier has determined that variance of the population of all cylindrical engine part outside diameters produced by current machine is appx. equal to, but no less than, .0005. To reduce this viariance, a new machine is designed, and random sample of n=25 outside diameters produced by this new machine has the mean x(bar)= 3 and a variance of s(squared)=.00014. Suppose the population of all cylindrical engine part outside diameters that would be produced by new machine is normally distributed, and let σ(squared) denote the variance of this popluation.
Test Ho: σ^2= .0005 vs Ha:σ^2<.0005 by setting α= .05