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.

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The sample proportion $\hat{p}$ is considered a consistent estimator of the population proportion $p$ because it is unbiased (its expected value equals the parameter it estimates, $p$), and its variance, $p(1-p)/n$, decreases as the sample size $n$ increases, leading to increased precision in the estimate as more data is collected.

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