Final answer:
To calculate the 95% confidence interval for the ratio of the population variances, determine the degrees of freedom for each sample and find the corresponding F-distribution critical values. These critical values, along with the sample variances, are used to calculate the confidence interval endpoints.
Step-by-step explanation:
The calculation of the confidence interval for the ratio of the population variances requires finding the critical values using an F-distribution because we are dealing with variances, not means. Here, we are given sample sizes n1=7 and n2=20, and sample variances s12=124.286 and s22=107.143, with a 95% level of confidence. First, we must identify the degrees of freedom for each sample, which are df1=n1-1 and df2=n2-1. Subsequently, we will use these degrees of freedom to find the critical values Fleft and Fright from the F-distribution table corresponding to the 95% confidence interval.
For our data, this means df1=6 and df2=19. The critical F-values are found based on these dfs and the desired level of confidence. Given a 95% confidence level, our two-tailed interval will require F-values that cut off the lower 2.5% and the upper 2.5% of the probability under the F-curve. The confidence interval for the ratio of variances is then calculated as s12/s22 multiplied by the inverse of the critical values of the F-distribution.
Once the critical values have been found, we can multiply these by our ratio of sample variances to find the left and right endpoints of the confidence interval. It's important to note that these computations might require access to statistical software or F-distribution tables.