Let p denote the proportion of individuals in a population who possess a specified property, and let X denote the number of individuals in the sample who possess the same property. Provided that the sample size n is large, the estimator $\hat { p } = \bar{X} / n$ has approximately
A) a normal distribution
B) a binomial distribution
C) an exponential distribution
D) a Poisson distribution

Question

Quizplus · Accepted Answer

When the sample size is large, according to the Central Limit Theorem, the sampling distribution of the sample proportion ($\hat{p}$) will be approximately normal, regardless of the distribution of the population, as long as the conditions of independence and large sample size are met. This is why option A is correct.

Let P Denote the Proportion of Individuals in a Population p^=Xˉ/n\hat { p } = \bar{X} / np^​=Xˉ/n

Let P Denote the Proportion of Individuals in a Population $\hat { p } = \bar{X} / n$