Question

Interpret the sample proportion, p+ , as a sample mean.

Answer 1

A sample proportion is a random variable: it varies from sample to sample in a way that cannot be predictedwith certainty. Viewed as a random variable it will be written p' it has mean

μP^ and a standard deviation .σP^. Here are formulas for their values.

Suppose random samples of size n are drawn from a population in which the proportion with a characteristic of interest is p. The mean μP^ and standard deviation σP^ of the sample proportion P^ satisfy

μPˆ=p  and  σPˆ=√pqn  

where q=1−p.