Question

The manager of a company wants to collect data to estimate the average sales of his salesmen in his company. A simple random sample of 100 employees has been collected out of 500 employees. At a​ 99.9% confidence, suppose the mean estimate for sales by his salesmen is between​ Rs.15,000 and​ Rs.35,000. Suppose that the population mean sales by the employee is​ Rs.14,000. Is this​ correct? Explain.

Choose the correct answer below.

A.The mean estimate by the salesman is incorrect because the value of

muμ

is not included within the confidence interval estimate.

B.The mean estimate by the salesman is correct because the value of

muμ

is included within the confidence interval estimate.

C.The mean estimate by the salesman is correct because the value of

muμ

is the midpoint of the confidence interval estimate.

D.The mean estimate by the salesman is incorrect because the value of

muμ

is not the midpoint of the confidence interval estimate.

Answer 1

For testing the hypothesis, we need to check whether the population mean lies in the range of the confidence interval with the given level of significance

As here the range of the confidence interval is between​ Rs.15,000 and​ Rs.35,000, and further population mean is Rs. 14,000.

As population mean do not lies in the range of CI, the mean estimate by the salesman is incorrect.

Hence answer here is

A.The mean estimate by the salesman is incorrect because the value of muμ

is not included within the confidence interval estimate.