When the two sample sizes are equal the denominator of 35 in

When the two sample sizes are equal, the denominator of (3.5) involves 2pbarqbar, whereas the denominator of (3.15) involves p1q1 + p2q2. Prove that p1q1 + p2q2 is less than or equal to 2pbarqbar when n1=n2, with equality if and only if p1=p2.

(3.15)   Z’= (| p2-p1| -.5(1/n1 + 1/n2))/sqrt((p1q1/n1) + (p2q2/n2))

(3.5)    Z=(|p2-p1|-.5(1/n1 + 1/n2))/sqrt((pbarqbar(1/n1 +1/n2))

Solution