Chapter 10.3, Problem 30E

In Exercises 29 and 30, construct the confidence interval for ${\sigma }_1^2/{\sigma }_2^2$. Assume the samples are random and independent, and the populations are normally distributed.

30. Cholesterol Contents In a recent study of the cholesterol contents of grilled chicken sandwiches served at fast food restaurants, a nutritionist found that random samples of sandwiches from Restaurant A and from Restaurant B had the sample statistics shown in the table. Construct a 95% confidence interval for ${\sigma }_1^2/{\sigma }_2^2$, where ${\sigma }_1^2$ and ${\sigma }_2^2$ are the variances of the cholesterol contents of grilled chicken sandwiches from Restaurant A and Restaurant B, respectively.

Cholesterol contents of grilled chicken sandwiches
Restaurant A	Restaurant B
$s_1^2$= 5.29	$s_2^2$ = 3.61
n1 = 16	n2 = 12