Sandpaper is rated by the coarseness of the grit on the paper. Sandpaper that is more coarse will remove material faster. Jobs such as the final sanding of bare wood prior to painting or sanding in between coats of paint require sandpaper that is much finer. A manufacturer of sandpaper rated 220, which is used for the final preparation of bare wood, wants to make sure that the variance of the diameter of the particles in their 220 sandpaper does not exceed 2.0 micrometers. Fifty-one randomly selected particles are measured. The variance of the particle diameters is 2.13 micrometers. Assume that the distribution of particle diameter is approximately normal.
a. Construct the 95% confidence intervals for the population variance and standard deviation.
b. Test at a 2.5% significance level whether the variance of the particle diameters of all particles in 220-rated sandpaper is greater than 2.0 micrometers.