You are given the sample mean and the population standard de

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 35 home theater systems has a mean of $125.00. Assume the population standard deviation is $18.80.

Construct a 90% confidence interval for the population mean.

The 90% confidence interval for the population mean ( , ) Round to two decimal places as needed

Construct a 95% confidence interval for the population mean.

The 95% confidence interval for the population mean ( , ) Round to two decimal places as needed

Solution

A random sample of 35 home theater systems has a mean of $125.00. Assume the population standard deviation is $18.80.

Construct a 90% confidence interval for the population mean.

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

18.8

Sample Mean

125

Sample Size

35

Confidence Level

90%

Intermediate Calculations

Standard Error of the Mean

3.1778

Z Value

-1.6449

Interval Half Width

5.2270

Confidence Interval

Interval Lower Limit

119.77

Interval Upper Limit

130.23

we are 90% confident that population mean will fall in the interval (119.77,130.23)

Construct a 95% confidence interval for the population mean.

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

18.8

Sample Mean

125

Sample Size

35

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

3.1778

Z Value

-1.9600

Interval Half Width

6.2283

Confidence Interval

Interval Lower Limit

118.77

Interval Upper Limit

131.23

we are 95% confident that population mean will fall in the interval (118.77,131.23)

95% CI is wider than 90% CI

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	18.8
Sample Mean	125
Sample Size	35
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	3.1778
Z Value	-1.6449
Interval Half Width	5.2270
Confidence Interval
Interval Lower Limit	119.77
Interval Upper Limit	130.23