SOLUTION: The standard deviation of a variable is 15. if a sample of 100 individuals is selected, compute the standard error of the mean. What size sample is necessary to double the standard

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Question 322202: The standard deviation of a variable is 15. if a sample of 100 individuals is selected, compute the standard error of the mean. What size sample is necessary to double the standard error of the mean?
I got the answer to that question. It is n=25.
This is the question I need help with...
What size sample is needed to cut the standard error of the mean in half?
Hope you can help, Thank you! :)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The standard deviation of a variable is 15.
if a sample of 100 individuals is selected, compute the standard error of the mean.
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standard error = 15/sqrt(100) = 1.5
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What size sample is necessary to double the standard error of the mean?
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Solve: 10/sqrt(n) = 2*1.5
10/sqrt(n) = 3
sqrt(n) = 10/3
n = (10/3)^2
n = 100/9 = 11.11
Round up to n = 12
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What size sample is needed to cut the standard error of the mean in half?
Solve 10/sqrt(n) = 3/4
sqrt(n) = 10/(3/4)
sqrt(n) = 40/3
n = (40/3)^2
n = 178 when rounded
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Cheers,
Stan H.