How to Find the Minimum Sample Size You Should Use to Assure a Specific Margin
When sampling for statistical evaluation, it makes sense to use the smallest possible sample size that will give the margin of error you can tolerate. Choosing the smallest possible sample is important because it saves time, money and effort. When sampling to calculate the confidence interval for the mean of a population, there is a basic equation you can use. All you need to know to solve the equation are the degree of confidence you want for our results and the acceptable margin of error.
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Instructions
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Calculating Minimum Sample Size
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Decide on the margin of error that you can tolerate in the calculated confidence interval for the mean of the population you are sampling. This margin of error is the "window" within which you will conclude your true population mean lies. For example, if the confidence interval for the mean rainfall per year in a region is 26 inches plus or minus 2 inches, 2 would be the margin of error. A smaller margin of error means that your confidence interval is narrower, but this requires a larger sample size. The margin of error is abbreviated as "E."
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2
Decide on the level of confidence you want for the calculated confidence interval. Convert this to a decimal format and subtract from 1 to determine the alpha value for your interval. Alpha times 100 is the percent chance that your calculated confidence interval will not actually include the true population mean. So a 95 percent confidence level would have an alpha value of 1 - 0.95 = 0.05.
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3
Calculate the Z(alpha/2) value for this alpha by first dividing alpha by 2 then subtracting this value from 0.5. Then look up the resulting value in the interior of the Z table and find the corresponding Z(alpha/2). In our example using alpha of 0.05, alpha/2 = 0.025 and 0.5 - 0.025 = 0.475. The Z(alpha/2) value corresponding to this obtained from the Z table is 1.96.
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4
Estimate the standard deviation -- sigma -- of the population being sampled. To do so, take the lowest known value of the population and subtract it from the highest known value, then divide by 6. So if the lowest recorded annual rainfall in a region was 2 inches and the highest was 112 inches, we would approximate sigma as (112 - 2)/6 = 18.3.
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Calculate the minimum required sample size (n) using the equation n = {[Z(alpha/2)]^2 x sigma^2}/E^2.
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Tips & Warnings
If your calculated value of n is not an integer (for example, n = 3.2), use the next highest integer as your sample size (n = 4) to ensure the desired margin of error is obtained.
This approach requires an approximation of the standard deviation of the population. This approximation requires that you assume the population you are sampling has a normal distribution.
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