SOLUTION: An IQ test is designed to let the mean is 100 and the standard deviation is 12 the population of normal adults. Find the sample size necessary to estimate the mean IQ score of nurs
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Question 1198440: An IQ test is designed to let the mean is 100 and the standard deviation is 12 the population of normal adults. Find the sample size necessary to estimate the mean IQ score of nurses such that it can be said with 95% confidence that the sample is within 2 IQ points of the true mean. Assume that the standard deviation is 12 and determine the required to emphasize using technology and determine if this is the reasonable sample size of the real world calculation Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the z-score formula used is:
z = (x-m)/s
z is the z-score
x is the raw score
m is the mean
s is the standard error = standard deviation / sqrt(n)
n is the sample size
when standard deviation is 12, s = 12 / sqrt(n)
if you want the solution to be within 2 points, then (x-m) must be equal to 2.
z-score formula becomes:
z = 2/(12/sqrt(n))
at 95% confidence interval, the critical z-score is plus or minus 1.96
on the high side, the formula becomes:
1.96 = 2 / (12/sqrt(n))
this becomes:
1.96 = 2 * sqrt(n) / 12
multiply both sides of the equation by 12 and divide both sides of the equation by 2 to get:
1.96 * 12 / 2 = sqrt(n)
solve for sqrt(n) to get:
sqrt(n) = 11.76
solve for n to get:
n = 11.76^2 = 138.2976.
n must be an integer, so round up to 139.
that's your minimum sample size required to get a margin of error within 2 IQ points.
your standard error becomes 12 / sqrt(139) = 1.017826716.
using that standard of error, absolute value of your margin of error will be 2.
that means it will be less than 2 and greater than -2.
it doesn't matter what the population mean is, as long as the standard error is equal to 1.017826716.
to confirm, i used a mean of 100 with that standard error to get:
raw scores are between 98.005 and 101.995.
since the mean is 100, the margin of error is minus 1.005 and 1.995.
that is less than -2 and 2.
