Two large home improvement stores advertise that they sell their paint at the same average price per gallon. A random sample of 25 cans from store Y had a standard deviation of $5.21, and store Z had a standard deviation of $4.08 based on a random sample of 20 cans. At α=0.05, can we conclude that the variances are different? How much less would store Z’s standard deviation have to be in order to conclude a difference?

For each exercise, perform these steps. Assume that all variables are normally or approximately normally distributed.

a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.