Key Concepts

• The distribution of the sample proportion follows a normal distribution with a mean of [latex]\mu = np[/latex] and a standard deviation of [latex]\sigma = \sqrt{np(1-p)}[/latex]. This is because the distribution of a sample proportion is based on the binomial probability distribution.
• [latex]P’[/latex] (read “p prime) is the sample proportion (point estimate) for a confidence interval for a population proportion.
• The error bound formula is [latex]z (\sqrt{\frac{p' q'}{n}})[/latex], where [latex]q'=1-p'[/latex].
• The “plus-four” method of adding two additional successes and two additional failures can be used to produce more accurate confidence intervals.

Glossary

binomial probability distribution: a discrete random variable (RV) that arises from Bernoulli trials; there are a fixed number, n, of independent trials. The notation is: [latex]X \sim B(n, p)[/latex]. The mean is [latex]\mu =np[/latex] and the standard deviation is [latex]\sigma = \sqrt{np(1-p)}[/latex].

error bound for a population proportion (EBP): the margin of error; depends on the confidence level, the sample size, and the estimated (from the sample) proportion of successes