Estimators and the sampling distribution of a sample proportion

What the exam asks

Core ideas

Point estimators and unbiasedness

A point estimator is a statistic (a rule or formula, such as $\hat{p}$) used to predict the value of an unknown population parameter (such as $p$). The specific number calculated from a particular sample is the point estimate.

An estimator is unbiased if the mean of its sampling distribution equals the true value of the population parameter being estimated. For a sample proportion:

Because the average of $\hat{p}$ across all possible random samples of size $n$ equals $p$, the sample proportion $\hat{p}$ is an unbiased estimator of the population proportion .

Center, variability and shape of the sampling distribution of $\hat{p}$

Suppose we select random samples of size $n$ from a population where the true proportion of successes is $p$. The sampling distribution of $\hat{p}$ displays the values of $\hat{p}$ from all possible samples of the same size from that population.