To construct a confidence interval for a proportion , it is not necessary to substitute for the unknown value of in the formula

To construct a confidence interval for a proportion

π, it is not necessary to substitute πˆ for the unknown value of π in the formula for the true standard error of πˆ . A less approximate method (called the score confidence interval for a proportion) finds the endpoints for a 95% interval by determining the π values that are 1.96 standard errors from the sample proportion, by solving for π in the equation

For Example 5.8 (page 137) with no vegetarians in a sample of size 20, substitute πˆ and n in this equation and show the equation is satisfied at π = 0 and at π = 0.161.

So, the 95% confidence interval is (0, 0.161), compared to (0, 0)

based on the ordinary formula.

|-|=1.96 (1-) n