Question

# You are given the sample mean and the population standard deviation. Use this information to construct...

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.)

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.

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