confidence interval question

Question

In an experiment to assess the effects on rats of exposure to cigarette smoke, 11 animals were exposed and 11 control animals were not exposed to smoke from unfiltered cigarettes. At the end of the experiment, measurements were made of the frequency of the ciliary beat (beats/min at 20◦C) in each animal. The variance for the exposed group was 3400 and 1200 for the unexposed group.

Find a 99% confidence interval for the ratio of these variances.

Do these data indicate that in the populations represented, the variances are truly different?

Answer 1

F-value for alpha/2 = 0.005 and 10,10 degrees of freedom = 5.85

F-value for 1 - alpha/2 = 0.995 and 10,10 degree of freedom = 0.171

CI = 3400/1200 var1/var2 3400/12

---------------< < -----------

5.85 0.171