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 concern about product quality.
Thickness measurements for a random sample of 10 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.