Sample size for confidence intervals on the mean

The BIS.Net Team BIS.Net Team

To determine the sample size for a confidence interval to have a specified margin-of-error we need to apply the following formula.

N = Z_Value(alpha / 2) * Sigma / (margin-of-error)^2

Where alpha is the specified level of significance. For a 95% confidence interval alpha =.05 as derived from (100-percent)/100

Z-Value is the Z score obtained from Normal Probability Tables

Sigma is the known standard deviation and margin-of-error the specified value. The actual confidence interval width will be equal to 2 times margin-of-error .

Because the expression Z_Value(alpha / 2) * Sigma / (margin-of-error)^2 will be a non-integer number, whereas the computed sample size must be an integer, the actual margin of error will be slightly different to the specified value.

BIS.Net Analyst therefore recalculates the margin of error using the calculated integer sample size and following formula

AME = Z_Value(alpha / 2) * Sd / Sqrt(N)

Provided the resultant sample size is large, the above formula is robust to departures in normality.

The formula does require a known standard deviation.

It is possible to fall into the trap of using t values instead of z values. T values are appropriate when calculating confidence intervals if the standard deviation is unknown. But to use a sample standard deviation and t value obtained prior to new sampling is dubious because the sample result is unlikely going to equal the prior sample standard deviation and hence is not a BIS.Net Analyst option.

Analysts need to obtain an estimate of the standard deviation from historical information. If this is not available then there is no choice but to take a large sample too obtain a standard deviation for future confidence intervals. The required sample size can be estimated by selecting Standard Deviation from the dropdown box.

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