# Confidence Interval question

1. Aug 3, 2010

### Gekko

1. The problem statement, all variables and given/known data

I re-wrote a previous thread just to make it clearer:

Construct a normal symmetric 100(1-alpha)% confidence interval [L,R] for p then show that [L,1] is then an approximate 100(1-alpha/2)% confidence interval for p

The normal distribution ranges from 0 to 1

3. The attempt at a solution

(1-alpha) = integral from L to R of e^-u^2 du. This means alpha = 1-integral from L to R of e^-u^2 du = integral from -inf to L of e^-u^2 + integral from R to inf of e^-u^2

When R=1, integral from L to inf of e-u^2 du = (1-beta). beta = 1- integral from -inf to L of e^-u^2 du. Since symmetric, beta = alpha /2