Question: 6.You are given the sample mean and the population standard deviation. Use this information to construct the90% and95% confidence intervals for the population mean. Interpret

6.You are given the sample mean and the population standard deviation. Use this information to construct the90% and95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. Ifconvenient, use technology to construct the confidence intervals.

A random sample of 40 home theater systems has a mean price of $114.00. Assume the population standard deviation is $16.50.

Construct a90% confidence interval for the population mean.

The90% confidence interval is (____,____).

(Round to two decimal places asneeded.)

Construct a95% confidence interval for the population mean.

The95% confidence interval is (____,_____).

(Round to two decimal places asneeded.)

Interpret the results. Choose the correct answer below.

A.With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is narrower than the90%.

B.With90% confidence, it can be said that the population mean price lies in the first interval. With95% confidence, it can be said that the population mean price lies in the second interval. The95% confidence interval is wider than the90%.

C.With90% confidence, it can be said that the sample mean price lies in the first interval. With95% confidence, it can be said that the sample mean price lies in the second interval. The95% confidence interval is wider than the90%.

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