A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is .3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a variance of .4 inches. State the null and alternative hypotheses, compute the test statistic, state your decision rule, and draw conclusions if necessary.
a. Construct a 95% confidence interval for the population variance.
b. Construct a 95% confidence interval for the population standard deviation.
c. Test at the 5% level of significance whether the variance of the length of pipes is significantly different from the standards