One recent study showed that the average annual amount spent by an East Coast household on frankfurters was $23.84 compared with an average of $19.83 for West Coast households. Suppose a random sample of 11 East Coast households showed that the standard deviation of these purchases (frankfurters) was $7.52, whereas a random sample of 15 West Coast households resulted in a standard deviation of $6.08.Do these samples provide enough evidence to conclude that the variance of annual frankfurter purchases for East Coast households is greater than the variance of annual frankfurter purchases for West Coast households? Let alpha be .05.
Assume amounts spent per year on frankfurters are normally distributed. Suppose the data did show that the variance among East Coast households is greater than that among West Coast households. What might this variance mean to decision makers in the frankfurter industry?