An auto manufacturing company wants to estimate the variance of miles per gallon for its auto model AST727. A random sample of 22 cars of this model showed that the variance of miles per gallon for these cars is .62. Assume that the miles per gallon for all such cars are (approximately) normally distributed.
a. Construct the 95% confidence intervals for the population variance and standard deviation.
b. Test at a 1% significance level whether the sample result indicates that the population variance is different from .30.