The sample proportion $\hat { p }$ is a consistent estimator of the population proportion p because it is unbiased and the variance of $\hat { p }$ is p(1 - p)/n, which grows smaller as n grows larger.

Question

Quizplus · Accepted Answer

The statement is true. A consistent estimator is one that approaches the true parameter as the sample size increases. The sample proportion is an unbiased estimator of the population proportion and has a lower variance as the sample size increases (as shown by the formula given). Therefore, it is a consistent estimator of the population proportion.

The Sample Proportion p^\hat { p }p^​ Is a Consistent Estimator of the Population Proportion P Because

The Sample Proportion $\hat { p }$ Is a Consistent Estimator of the Population Proportion P Because