Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. If the true variance in thicknesses exceeds 2.25 square millimeters, there is cause for concem about product quality. Thickness measurements for a random sample of ten sheets produced in a particular shift were taken, giving the following results (in millimeters): 226 226 232 227 225 228 225 228 229 230

(a) Find the sample variance.

(b) Test at the 5% significance level the null hypothesis that the population variance is at most 2.25.