Consider the hypothesis test given by 05 05 1 0 H p H p In

Consider the hypothesis test given by : 0.5 : 0.5 1 0 H p H p In a random sample of 400 subjects, the sample proportion is found to be p ˆ 0.55.

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work;

(c) Is there sufficient evidence to justify the rejection of H0 at the 0.01 level?

Explain

Solution

Ho:p1=p2 against H1:p1<p2(it is left tail)

Given p1=0.5, p2=0.510, n=400(large sample, and assume n1=n2=200), P^=0.55, Q^=1-P^=1-0.55=0.45. The table value of Z at 0.01(left tail) is -2.33. Then Zcal =(p1-p2)/[P^*Q^*((1/n1)+(1/n2))]=(.5-.51)/[.55*.45*.01]=-0.01/0.0497=-0.2012. Here Zcal>Ztab, so we reject null hypothesis, i.e.,we accept H1:p1<p2.