Question

You are given the sample mean and the sample 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 5050 home theater systems has a mean price of ​$145.00145.00 and a standard deviation is ​$18.7018.70.

The​ 90% confidence interval is

The​ 95% confidence interval is

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 statistical software output for this problem is:

Hence,

90% confidence interval: (140.57, 149.43)

95% confidence interval: (139.69, 150.31)

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%. Option C is correct.