63. Let X1 and X2 be binomial random variables with respective parameters n1, p1 and n2, p2. Show that when n1 and n2 are large, an approximate level α test of H0 : p1 = p2 versus H1 : p1 = p2 is as follows:

Hint:

(a) Argue first that when n1 and n2 are large

where ∼˙ means “approximately has the distribution.”

(b) Now argue that when H0 is true and so p1 = p2, their common value can be best estimated by (X1 + X2)/(n1 + n2).

[X/n1 - X/n2 reject Ho if X1+X2 n1+n2 (1) X1 + X2 * ) (+) n1 + 72 > Zal2