Question

Independent random samples of n = 150 and n = 150 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 68 successes, and sample 2 had 74 successes. You wish to perform a hypothesis test to determine if there is a difference in the sample proportions P, and py: (a) State the null and alternative hypotheses. O Ho: (P1 - P2) = 0 versus Ha: (P1-P2) < 0 O Ho: (2,-) < versus H: (2,-2) > 0 O Ho: (P1-P2) = 0 versus H : (P1-P2) > 0 HO: (P1-P2) # O versus H: (P1-P2) = 0 O Ho: (P1-P2) = 0 versus H : (P1-P2) = 0 (b) Find the test statistic and rejection region, using the a = 0.10 level of significance. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.) test statistic z = rejection region 2 > ν (c) State your conclusion. O He is not rejected. There is insufficient evidence to indicate that p, is different from P. O He is not rejected. There is sufficient evidence to indicate that p, is different from Pz: O Hois rejected. There is sufficient evidence to indicate that p, is different from py O Ho is rejected. There is insufficient evidence to indicate that P, is different from P2

Answer 1

a)

O Ho: (-P2) = 0 versus Hy: (P1-P2) = 0

b)

x1                =	68	x2                =	74
p̂1=x1/n1 =	0.4533	p̂2=x2/n2 =	0.4933
n1                       =	150	n2                       =	150
estimated prop. diff =p̂1-p̂2    =		-0.0400
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.4733
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0577
test stat z=(p̂1-p̂2)/Se =		-0.69

rejection region : z>1.64

z< -1.64

c)

since test statistic is not in rejection region:

O H, is not rejected. There is insufficient evidence to indicate that p, is different from pa