You are given the sample mean and the population standard deviation. Use this in
ID: 3428306 • Letter: Y
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 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
Explanation / Answer
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
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