Question

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 of 20 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. And a random sample of 24 turkeys sold at the chain's stores in Charlotte yielded a sample mean of 14.89 pounds, with a sample standard deviation of 2.7 pounds. Use a 5% 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 use the pooled t-test. (15 points)

Answer 1

Let , be the population average weight of turkeys sold in Detroit and be the population average weight of turkeys sold in charlotte.

Hypothesis: Vs   (Claim)

Since , the population standard deviations are equal.

Therefore , use t-test.

Now , df=n1+n2-2=20+24-2=42

The pooled estimate is ,

The test statistic is ,

The critical value is ,

; Teh Excel function is , =TINV(0.05,42)

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , Reject Ho.

Conclusion : Hence , there enough evidence to conclude that there is a difference in the mean weight of turkeys sold in these two cities.