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 60 home theater systems has a mean price of $113.00. Assume the population standard deviation is $17.90. Construct a 90% confidence interval for the population mean
Answers
Solution :
Given that,
(a)
At 90%
Z
/2 = 1.645
Margin of error = E = Z
/2* (
/
n)
= 1.645 * (17.90 /
60)
= 3.80
At 90% confidence interval estimate of the population mean is,
- E <
<
+ E
113 - 3.80 <
< 113 + 3.80
109.2 <
< 116.80
(109.2 , 116.80)
(ii)
At 95%
Z
/2 = 1.96
Margin of error = E = Z
/2* (
/
n)
= 1.96 * (17.90 /
60)
=4.53
At 95% confidence interval estimate of the population mean is,
- E <
<
+ E
113 - 4.53 <
< 113 + 4.53
108.47 <
< 117.53
(109.2 , 116.80)
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