A loan officer intends to compare the interest rate for 48-month fixed-rate auto loans and 48-month variable-rate auto loans. She selects two independent random samples of 48-month auto loans and observes the following loan rates: Fixed rate(6) Variable rate(96) 10.29 9.59 9.75 8.75 9.50 8.99 9.99 8.50 9.75 9.00 9.99 11.4 10.00 a) Estimate and interpret the ratio of the population variances of the interest rates for 48-month fixed-rate and variable-rate auto loans with 90% confidence. b) Carry out an appropriate hypothesis test at the 5% significance level to see whether the population variance of the fixed-rate 48-months auto loans likely exceeds the population variance of the variable-rate 48-months auto loans. Briefly discuss the steps of the test showing all relevant details. c) What conditions are required by the confidence interval estimator and the hypothesis test in parts (a) and (b)? Are they likely satisfied? Explain your