1. The estimate of the proportion (“p-hat”) based on the sample can be a variety of values, and we don’t expect to get the same value every time, but the possible values we could get follows a probability distribution. (This is the sampling distribution.)
The expected value of that probability distribution is the proportion in the population (p, the “parameter”).
The variance of that probability distribution is p(1-p)/n. (This is the sampling variability.)
The variability is lower for larger sample sizes (n).
The variability is highest when p=.5 and lowest when p is close to 0 or 1.
If the sample size is large enough, the distribution of the estimate will be approximately Normal.
For the estimate to be approximately Normally distributed, we need a larger sample size the further p is from Rule of thumb: Need np≥10 and n(1-p)≥10.