## Sample Sizes – Surveys

**Introduction**

How many responses are needed for a survey? This question requires specifying the desired confidence and the accuracy of the survey results.

**The Bernoulli Trial**

A Bernoulli trial is an event that has two possible outcomes. Consider the case where the only possible outcomes are success or failure. Let the probability of a success is p and the probability of failure equals q. The probabilities of all possible events must equal 1, so q = 1-p. These relationships are expressed mathematically as