For testing H 0 : 1 = 2 using independent binomial variates y 1 and y 2? with n 1 and n 2

For testing H₀: π₁ = π₂ using independent binomial variates y₁ and y_2? with n₁ and n₂ trials, the score statistic is

where π̂ = (y₁ + y₂)/(n₁ + n₂) is the pooled estimate of π₁ = π₂ under H₀. Show that z² = X².

V (1 )(1/n + 1/n2)