Question
In: Statistics and Probability
A simple random sample of 60 items resulted in a sample mean of 90. The population...
A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is σ = 10. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.) (b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)
Solutions
Expert Solution
Solution :
Given that,
Z
/2
= 1.96
(a)
n = 60
Margin of error = E = Z/2*
(
/
= 1.96 * (10 /
= 2.53
At 95% confidence interval estimate of the population mean is,
- E < 
<
+ E
90 - 2.53 <
< 90 + 2.53
87.47 <
< 92.53
(87.47 , 92.53)
(b)
n = 120
Margin of error = E = Z/2*
(
/
= 1.96 * (10 /
= 1.79
At 95% confidence interval estimate of the population mean is,
- E <
<
+ E
90 - 1.79 <
< 90 + 1.79
88.21 <
< 91.79
(88.21 , 91.79)
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