A. What is the Population variance

B. Construct a 95% Confidence Interval

C. Can we conclude that a change has occurred?

D. Assume that sample size increased to 2000/64 defects are found. Would you change your answer to C?

So, as this is a binomial issue, for

A, I understand that Var(Population) = (0.04)(0.96) = 0.0384

However, for question B, when I construct the confidence interval should it be between the two differences

Δ = 0.04-0.032 =0.008

Hence,

CI = 0.008 ± 1.96 * [(0.032/0.968)/500 +(0.04)(0.96)]

as a binomial confidence interval between two population proportions using independent samples?

or, should it rather be

CI = 0.008 ± 1.96 * [(0.032/0.968)/500]?

Much confused... any help will be greatly appreciated thankyou...