Part Four: F-Test for Comparing Two Variances or Two Standard Deviations

(Question 1) A congresswoman takes a random sample of the rents in two of her districts to see if they are the same. The average rent in the first district is $519 with a standard deviation of $38 based on a sample of 16. The average rent in the second district is $486 with a standard deviation of $27 based on a sample of 18. A preliminary test indicates the underlying populations have equal variances. Assuming normal distribution, test for equality of population variances at a significance level of 0.05.

(Question 2) Company A claims its feed makes chickens grow plumper than feed from Company B. A poultry producer randomly selects 41 chickens fed on A and 26 chickens fed on B. He finds a mean weight in pounds of 4.3 for A with a standard deviation of 1.3 and a mean weight of 3.9 for B with a standard deviation of 0.96. An earlier test shows that the populations have equal variances. Assuming a normal distribution, test for equality of population variances at a significance level of 0.02.