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 ​$136.00. Assume the population standard deviation is ​$18.60.

a) The​ 90% confidence interval is ​____

b) The​ 95% confidence interval is ____

c) 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 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%.

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

Result:

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 ​$136.00. Assume the population standard deviation is ​$18.60.

a) The​ 90% confidence interval is ​ (131.8747, 140.1253)

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	18.6
Sample Mean	136
Sample Size	55
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	2.5080
Z Value	1.645
Interval Half Width	4.1253
Confidence Interval
Interval Lower Limit	131.8747
Interval Upper Limit	140.1253

b) The​ 95% confidence interval is (131.0844, 140.9156)

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	18.6
Sample Mean	136
Sample Size	55
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	2.5080
Z Value	1.9600
Interval Half Width	4.9156
Confidence Interval
Interval Lower Limit	131.0844
Interval Upper Limit	140.9156

c) 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%.