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 55 home theater systems has a mean price of ?$135.00. Assume the population standard deviation is ?$19.80.

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 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%.

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 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%.