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 60 home theater systems has a mean price of ​$118.00. Assume the population standard deviation is ​$19.60. Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.)

Construct a​ 95% confidence interval for the population mean.

The​ 95% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.)

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 wider 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 narrower than the​ 90%.

Answer 1

Given that, a random sample of 60 home theater systems has a mean price of ​$118.00. Assume the population standard deviation is ​$19.60.

Using TI-84 calculator we find comfidence interval for population mean.

i) The​ 90% confidence interval is, (113.84, 122.16)

ii) The​ 95% confidence interval is, (113.04, 122.96)

Interpretation of above confidence intetvals,

With​ 90% confidence, it can be said that the population mean price lies in the first interval ( 113.84, 122.16). With​ 95% confidence, it can be said that the population mean price lies in the second interval (113.04, 122.96). The​ 95% confidence interval is wider than the​ 90%.

Answer: A)