For testing the difference between two proportions
is used as the approximate standard error of p̂1 - p̂2, where p̂c is the pooled sample proportion. Explain why this is reasonable when the null-hypothesized value of p1 - p2 is zero. Why would this not be a good approximation when the null-hypothesized value of p1 - p2 is a nonzero number? What would you recommend using for the standard error of p̂1 - p̂2 in that case?