1. Recall that for large n, the binomial distribution can be approximated by the normal distribution; that is for large n we may write, to good approximation, Z

∼=

nˆp − np 

np(1 − p)

or Z

∼=

ˆp − p 

p(1 − p)/n

∼ N(0, 1)

where ˆp is the observed sample proportion. What then, for n large, would be the approximate test of level α for testing

(a) p = p0 versus p = p1 > p0?

(b) p = p0 versus p = p0?