what is the formula to calculate the confidence interval of

what is the formula to calculate the confidence interval of two population proportions p1-p2 and why do we use this formula?

Solution

Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
p1 = Proportion of sample 1, P2 = Proportion of sample 2
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval

C.I for proportion is defined to = p ± M.E(P), Here marginof error is defined to

Margin of error = Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 ).