Question
In: Math
You may need to use the appropriate appendix table or technology to answer this question. A...
You may need to use the appropriate appendix table or technology to answer this question.
A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is
σ = 15.
(a)
Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)
( )to( )
(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.)
( )to( )
(c)
What is the effect of a larger sample size on the interval estimate?
A. A larger sample size does not change the margin of error.
B. A larger sample size provides a smaller margin of error.
C. A larger sample size provides a larger margin of error.
Solutions
Expert Solution
Solution:
Given: A simple random sample of 60 items resulted in a sample mean of 90.
The population standard deviation is σ = 15.
= 90
n = 60
Part a) Compute the 95% confidence interval for the population mean.
where
We need to find zc value for c=95% confidence level.
Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750
Look in z table for Area = 0.9750 or its closest area and find z value.
Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96
That is : Zc = 1.96
Thus
Thus
Part b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean.
n = 120
Thus
Part c) What is the effect of a larger sample size on the interval estimate?
B. A larger sample size provides a smaller margin of error.
milcah answered 1 year agoRelated Solutions
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