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 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%.

Answer 1

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%.