A national grocery store chain wants to test the difference in the average weight of turkeys sold in Detroit and the average weight of turkeys sold in Charlotte. According to the chain’s researcher, a random sample of20 turkeys sold at the chain’s stores in Detroit yielded a sample mean of 17.53 pounds, with a sample standard deviation of 3.2 pounds. Her random sample of 24 turkeys sold at the chain’s stores in Charlotte yielded a sample mean of14.89 pounds, with a sample standard deviation of 2.7 pounds.
Use a 1% level of significance to determine whether there is a difference in the mean weight of turkeys sold in these two cities. Assume the population variances are approximately the same and that the weights of turkeys sold in the stores are normally distributed.