Let’s look at taking a complete sampling distribution – that is, finding every sample of a certain size.

Four people responded to a yes/no survey question. The answers, and the population, are {yes, yes, yes, no}.

All the samples of size 2 are:

{yes, yes}

{yes, yes}

{yes, no}

{yes, yes}

{yes, no}

{yes, no}

The number of “yes” answers are analyzed.

The population proportion is .

The sampling distribution of the proportion is .

The mean of the sampling distribution of the proportion is the population proportion.