#### Theory of Sample Size Determination

Sample Size Determination:

The determination of sample size formula comes from the formulas for maximum error of the estimates. The formula is resolved for n. Be sure to round the answer obtained up to the next whole number, not off to the nearest whole number. If you round off, then you will exceed your maximum error of the estimate in some cases. By rounding off, you will encompass a smaller maximum error of the estimate than permitted; however this is better than containing a bigger one than desired.

Population Mean:

N = [(zα/2 σ)/E]2

The formula above for the sample size that is obtained by resolving the maximum error of estimate formula for the population mean for n.

Population Proportion:

N = [(zα/2)/E]2 pq

The formula above for the sample size that is obtained by resolving the maximum error of estimate formula for the population proportion for n. Some of the texts utilize p hat and q hat, however as the sample has not been taken, there is no value for sample proportion. p and q are taken from a prior study, if one is accessible. When there is no prior study or estimate accessible, then utilize 0.5 for p and q, as such are the values that will provide the maximum sample size, and it is better to encompass too large of a sample size and come beneath the maximum error of estimate than to encompass too small of a sample size and surpass the maximum error of the estimate.

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