Question

Testing the Difference Between Two Proportions. In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent.

9. Young Adults In a survey of 1750 females ages 20 to 24 whose highest level of education is completing high school, 64.4% were employed. In a survey of 2000 males ages 20 to 24 whose highest level of education is completing high school, 73.2% were employed. At a = 0.01, can you support the claim that there is a difference in the proportion of those employed between the two groups?

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

b)

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

c)

p1cap = 0.644
p1cap = 0.732
pcap = (X1 + X2)/(N1 + N2) = (1127+1464)/(1750+2000) = 0.6909

z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.644-0.732)/sqrt(0.6909*(1-0.6909)*(1/1750 + 1/2000))
z = -5.82

d)

Reeject Ho

e)

There is sufficient evidence to conclude that there is a difference in the proportion of those employed between the two groups