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 6060 home theater systems has a mean price of ​$135.00135.00. Assume the population standard deviation is ​$15.8015.80. 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 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

Answer 1

The provided sample mean is Xˉ=135

and the population standard deviation is σ=15.80.

The size of the sample is n = 60

and the required confidence level is 90%.

Based on the provided information, the critical z-value for

α=0.1 is z_c = 1.645

The 90% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 90 % confidence for the population mean μ is

The provided sample mean is Xˉ=135

and the population standard deviation is σ=15.80.

The size of the sample is n = 60

and the required confidence level is 95%.

Based on the provided information, the critical z-value for

α=0.05 is z_c = 1.96

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

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