A random sample of 20 nominally measured of the length of a plastic ball is taken and the lengths are measured precisely. The measurements, in mm, are as follows: XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX...

A random sample of 20 nominally measured of the length of a plastic ball is taken and the lengths are measured precisely. The measurements, in mm, are as follows: 2.02 1.94 2.09 1.95 1.98 2.00 2.03 2.04 2.08 2.07 1.99 1.96 1.99 1.95 1.99 1.99 2.03 2.05 2.01 2.03 From the data, we calculate ∑ ? = 40.19, ∑ ? 2 = 80.7977 Assuming that the lengths are normally distributed with unknown mean ?, and unknown variance ? 2 i. find a 90% confidence interval for the variance ? 2 . Interpret your results. ii. find a 90% confidence interval for the standard deviation ? . Interpret your results.