What is the Approximate Confidence Interval for p?

[Gekko]

Homework Statement

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

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

 

[lippyka]

. Therefore, integral from -inf to L of e^-u^2 du = 1- alpha/2. This is the approximate 100(1-alpha/2)% confidence interval for p.