At Armco's steel plant in Middletown, Ohio, statistical quality-control methods have been used very successfully in controlling slab width on continuous casting units. The company claims that a large reduction in the steel slab width variance resulted from the use of these methods. Suppose that the variance of steel slab widths is expected to be 156 (squared units).
A test is carried out to determine whether the variance is above the required level, with the intention to take corrective action if it is concluded that the variance is greater than 156. A random sample of 25 slabs gives a sample variance of 175. Using α = 0.05, should corrective action be taken?