5.77.* To construct a confidence interval for a proportion , it is not necessary to substitute ...

5.77.* 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 125) 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.

Transcribed Image Text:

(1-) |-|= 1.96 n