Question

6. Testing Ho : p = 0.75 versus Ha : p > 0.75 when the sample has n = 20, ˆp = 0.50.

(a) Verify that the sample size is large

(b) Find the standard error for ˆp

(c) Find the value of the standardized z-test statistic

Answer 1

a)

here since np=0.75*20 =15 and n(1-p) =20*(1-0.75) =5 ; both are greater than 5; sample size is large

b)

std error   se =√(p*(1-p)/n) = sqrt(0.75*0.25/20) =

0.0968

c)

sample proportion p̂ = x/n=		0.5000
test stat z =(p̂-p)/√(p(1-p)/n)=(0.5-0.75)/0.0968 =		-2.58