Question

Suppose that a random sample of 100 men between the ages of 25 and 54 was selected and it was found that 85 were currently working. A similar sample of 100 women was selected and 72 were working. Complete parts a and b below. a. Using alpha α equals = 0.025​, can it be concluded that the proportion of men in this age group who are working differs from the proportion of women who are​ working?

Answer 1

H0: p1 - p2 = 0
Ha: p1 - p2 not equals to 0

Here, x1 = 85 , x2 = 72 , n1 = 100 , n2 = 100
p1cap = 0.85 , p2cap = 0.72

pcap = (x1 + x2)/(n1 + n2)
pcap = (85 + 72)/(100 + 100)
pcap = 0.785

Standard Error,
SE = sqrt(pcap * (1-pcap) * (1/n1 + 1/n2))
SE = sqrt(0.785 * (1-0.785) * (1/100 + 1/100))
SE = 0.0581

Test statistic,
z = (p1cap - p2cap)/SE
z = (0.85 - 0.72)/0.0581
z = 2.24

p-value = 2*P(z>2.24) = 0.0251

As p-value > 0.025, fail to reject H0
Tehre are not significant evidence to conclude that the re is difference in the proportion.