Question

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 40 home theater systems has a mean price of ​$129.00. Assume the population standard deviation is ​$16.60.

Interpret the results. Choose the correct answer below.

A. With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is narrower than the​ 90%.

B. With​ 90% confidence, it can be said that the sample mean price lies in the first interval. With​ 95% confidence, it can be said that the sample mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.

C. With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.

Answer 1

The correct option is (C)

We have given a random sample of 40 home theater systems with sample mean and also we have given the population standard deviation .

Calculation for the 90% confidence interval for population mean

                             

                             

                             

                             

Width of 90% confidence interval:

Calculation for the 95% confidence interval for population mean

                            

                            

                             

                              

Width of 95% confidence interval:

Clearly by looking at the width calculated for the 90% and 95% confidence interval, the 95% confidence interval is wider than the 90%.