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 (%)	Variable rate (%)
10.29	9.59
9.75	8.75
9.50	8.99
9.99	8.50
9.75	9.00
9.99
11.40
10.00

Using this data set perform the following tasks. Do all calculations ‘manually’, i.e., with a hand calculator without using R, Excel or any other software, showing the relevant formulas and the major steps.

1. 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.