Question

1. predict the election a polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. the researchers will report the sample proportion $hat{p}$ that favors the incumbent as an estimate of the population proportion $p$ that favors the incumbent. explain to someone who knows little about statistics what it means to say that $hat{p}$ is an unbiased estimator of $p$.

Explanation:

An unbiased estimator means that, on average, the sample statistic (here, \(\hat{p}\)) will equal the population parameter (here, \(p\)). If we took many random samples of likely voters, calculated \(\hat{p}\) for each, and averaged those \(\hat{p}\) values, that average would be equal to the true population proportion \(p\) of voters favoring the incumbent. So \(\hat{p}\) doesn't systematically overestimate or underestimate \(p\) across many samples.

Answer:

An unbiased estimator (here, \(\hat{p}\)) means that, over many random samples, the average of the sample proportions \(\hat{p}\) will equal the true population proportion \(p\) (i.e., \(\hat{p}\) does not systematically over/underestimate \(p\)).