If 50% of all the people in a population of 20000 people drink coffee in the morning, and if you were repeat the survey of 377 people ("Did you drink coffee this morning?") many times, then 95% of the time, your survey would find that between 45% and 55% of the people in your sample answered "Yes".

The remaining 5% of the time, or for 1 in 20 survey questions, you would expect the survey response to more than the margin of error away from the true answer.

When you survey a sample of the population, you don't know that you've found the correct answer, but you do know that there's a 95% chance that you're within the margin of error of the correct answer.

Try changing your sample size and watch what happens to the

*alternate scenarios*. That tells you what happens if you don't use the recommended sample size, and how M.O.E and confidence level (that 95%) are related.
To learn more if you're a beginner, read

In terms of the numbers you selected above, the sample size

**Basic Statistics: A Modern Approach**and**The Cartoon Guide to Statistics**. Otherwise, look at the**more advanced books**.In terms of the numbers you selected above, the sample size

*n*and margin of error*E*are given byx | = | Z(^{c}/_{100})^{2}r(100-r) |

n | = | ^{N x}/_{((N-1)E2 + x)} |

E | = | Sqrt[^{(N - n)x}/_{n(N-1)}] |

where

If you'd like to see how we perform the calculation, view the page source. This calculation is based on the Normal distribution, and assumes you have more than about 30 samples.

About

*N*is the population size,*r*is the fraction of responses that you are interested in, and*Z*(*c*/100) is the critical value for the confidence level*c*.If you'd like to see how we perform the calculation, view the page source. This calculation is based on the Normal distribution, and assumes you have more than about 30 samples.

About

**Response distribution**: If you ask a random sample of 10 people if they like donuts, and 9 of them say, "Yes", then the prediction that you make about the general population is different than it would be if 5 had said, "Yes", and 5 had said, "No". Setting the response distribution to 50% is the most conservative assumption. So just leave it at 50% unless you know what you're doing. The sample size calculator computes the critical value for the normal distribution. Wikipedia has good articles on statistics.
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