Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. Typically, a variance in thickness around 1.95 square millimeters is regarded as acceptable. As part of quality control, a random sample of 30 plastic sheets are taken and the sample variance is calculated to be 3.17. Assume that the population is normally distributed. Let a = 0.05. (a) Construct a confidence interval for population variance at (1 − a) confidence level. (b) Test against an upper-tail hypothesis that the true population variance is larger than 1.95.

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