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 45 home theater systems has a mean price of ​$120.00. Assume the population standard deviation is ​$17.50.

Answer 1

Solution:

The 90% and 95% confidence intervals for the population mean by using excel are given as below:

90% Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	17.5
Sample Mean	120
Sample Size	45
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	2.6087
Z Value	-1.6449
Interval Half Width	4.2910
Confidence Interval
Interval Lower Limit	115.71
Interval Upper Limit	124.29

95% Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	17.5
Sample Mean	120
Sample Size	45
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	2.6087
Z Value	-1.9600
Interval Half Width	5.1130
Confidence Interval
Interval Lower Limit	114.89
Interval Upper Limit	125.11

From above two observations, it is observed as we increase the confidence level, the margin of error increase, and therefore width of the confidence interval increases.