Question

Consider the following measures based on independently drawn samples from normally distributed populations: (You may find it useful to reference the appropriate table: chi-square table or F table) Sample 1: s21 = 241, and n1 = 26 Sample 2: s22 = 220, and n2 = 16 a. Construct the 95% interval estimate for the ratio of the population variances.

Answer 1

To construct a 95% interval estimate for the ratio of population variances, calculate the F statistic using the given sample variances and sample sizes, then use the F table to find the critical values. The 95% interval estimate is (1/F_upper, 1/F_lower).

Step-by-step explanation:

To construct a 95% interval estimate for the ratio of population variances, we need to use the F distribution. First, we calculate the F statistic using the given sample variances and sample sizes: F = ((s1^2)/n1) / ((s2^2)/n2). Plugging in the values, we get F = ((241^2)/26) / ((220^2)/16) ≈ 3.890. Using the F table, we find the critical values for a 95% confidence level with 25 and 15 degrees of freedom. The lower critical value is 0.346 and the upper critical value is 3.761.

The 95% interval estimate for the ratio of population variances is given by: (1/F_upper, 1/F_lower) = (1/3.761, 1/0.346) ≈ (0.266, 2.890). Therefore, we can estimate with 95% confidence that the ratio of the population variances is between 0.266 and 2.890.