For each of these problems, perform the following steps.

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.

The average price of a random sample of 12 bottles of diet salad dressing taken from different stores is $1.43. The standard deviation is $0.09. The average price of a random sample of 16 low calorie frozen desserts is $1.03. The standard deviation is $0.10. At α = 0.01, is there a significant difference in price? Find the 99% confidence interval of the difference in the means.