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 35 home theater systems has a mean price of ​$128.00 Assume the population standard deviation is ​$19.30

Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is

​(Round to two decimal places as​ needed.)

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

The​ 95% confidence interval is

​

​(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 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

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