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

Question

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

Quizplus · Accepted Answer

The statement is true. The sample proportion is an unbiased estimator of the population proportion, which means that on average, it will equal the true population proportion. Additionally, the variance of the sample proportion is p(1-p)/n, which means that the variance decreases as sample size increases. Both of these properties make the sample proportion a consistent estimator of the population proportion.

The Sample Proportion Is a Consistent Estimator of the Population