Sampling distributions for sample proportions

Learning objectives

Explain what makes a statistic an unbiased estimator of a parameter, decide from a simulated sampling distribution whether an estimator is biased, and use a sample statistic as a point estimate of a parameter

State the mean p and the standard deviation √(p(1 − p)/n) of the sampling distribution of a sample proportion, and explain why a larger sample reduces its variability without moving its center

Check the conditions for a normal model of a sample proportion: a random sample, a sample of no more than 10% of the population when sampling without replacement, and np and n(1 − p) both at least 10

Calculate and interpret the probability that a sample proportion falls in a given interval

State the mean p₁ − p₂ and the standard deviation √(p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂) of the sampling distribution of a difference between two sample proportions, check its conditions for two independent random samples or a randomized experiment, and calculate a probability for the difference