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 6060 home theater systems has a mean price of $129.00129.00. Assume the population standard deviation is ​$15.9015.90.

Construct a​ 90% confidence interval for the population mean.

The​ 90% confidence interval is ​(___,___​).

​(Round to two decimal places as​ needed.)

Answer 1

Solution:

No. Of sample = 60

Sample mean = 129

Population standard deviation = 15.90

90% confidence interval can be calculated as

Mean +/- Zalpha/2*SD/sqrt(n)

Zalpha/2 = 1.645

129+/-1.645*15.90/sqrt(60)

129 +/- 1.645*15.90/7.746

129 +/- 3.38

So 90% confidence interval is

125.62 to 132.38

We are 90% confidence that population mean is between 125.62 to 132.38

95% confidence interval can be calculated as

Zalpha/2= 1.96

129 +/- 1.96*15.90/7.746

129+/- 4.02

124.98 to 133.02

We are 95% confidence that population mean is in between 124.98 to 133.02

Here we can see that as confidence level increased than confidence interval width also increase.