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

3535

home theater systems has a mean price of

$124.00124.00.

Assume the population standard deviation is

$16.1016.10.

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Part 1

Construct a 90% confidence interval for the population mean.

The 90% confidence interval is

(enter your response here,enter your response here).

(Round to two decimal places as needed.)

Part 2

Construct a 95% confidence interval for the population mean.

The 95% confidence interval is

(enter your response here,enter your response here).

(Round to two decimal places as needed.)

Part 3

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 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%.

C.

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%.