Question

# You are given the sample mean and the population standard deviation. Use this information to construct...

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 ​\$115.00. Assume the population standard deviation is ​\$17.70.

1. The​ 90% confidence interval is?

2. 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%.

Given the sample size and sample mean , population standard deviation

The two sided confidence interval for mean based on the sample data is

1) With , the 90% confidence interval is

2)We are 90% confident that the population mean lies in the interval

With , the 95% confidence interval is

The correct option is:

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%.

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