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I was told that to calculate an approximate sample size, let n =[Z/2ME]^2; z=1.96 for a confidence level of .95.  Then n[1.96/2(.03)]^2 = 1,067.

My question is 1) where did we get ME from? 2) is this equation correct for calculating an approximate sample size?


First, in words, this problem is using the "normalized z-value" to obtain the sample size needed to make sure that the calculated mean (based on the samples) is within a specified interval around the population mean at a given confidence interval and given a known population standard deviation.

It is easier to see what's going on if we write down the formula for the normalized z-value, also known as the z-score:

let σ = population standard deviation (assumed given)

then σ_m = σ/√n = standard deviation of the mean m calculated using n samples

∆m = m - m_pop = difference between the calculated mean and m_pop = the given population mean.

Then, we are given that ∆m has to be small enough so that 95% of the time t will be smaller than

z = ∆m/σ_m.

This corresponds to z = 1.96.

Rearranging these expressions gives

n = [ (z・σ)/∆m ]^2.

Comparing with your formula,it looks like

σ/∆m = 1/(2ME) = 1/[ (2/(0.03) ]

This could mean that ME = ∆m = 0.03 and that σ = 1/2.

If this is true, then this is a correct method for calculating the sample size (to be correct, the method also requires a reasonably large sample size so that the statistics are approximately normal, which seems to be the case).  

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randy patton


college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography


26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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