A sociologist is studying the effect of having children within the first three y

Question

A sociologist is studying the effect of having children within the first three years of marriage on the divorce rate. From city marriage records, she selects a random sample of 400 couples who were married between 1985 and 1990 for the first time, with both members of the couple between the ages of 20 and 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within five years. Of the couples who didn't have children within the first three years, 52 were divorced. Among couples who had a child within the first three years, suppose p is the proportion who were divorced within five years. Similarly, among couples who did not have a child within the first three years, suppose p2 is the proportion who were divorced within five years. The sociologist had hypothesized that having children early would increase the divorce rate. If she tests the one-sided alternative with a 0.05 significance level, what is the correct conclusion? O There is not significant evidence that the proportion of those who divorce is higher for those having children early. O There is significant evidence that the proportion of those who divorce is the same whether having children early or not. O There is significant evidence that the proportion of those who divorce is higher for those having children early.

Explanation / Answer

H_0: p1=p2

H_1:p1>p2

n1=220
n2=400-220
p1 = 83/220
p2 = 52/(400-220)
SE=(p1*(1-p1)/n1)+(p2*(1-p2)/n2)
z = (p1-p2)/sqrt(SE) =1.88

z.alpha = 1.64

therefore z>z.alpha

reject Ho, which is significant
p.value=pnorm(q = 1.88,mean = 0,sd = 1,lower.tail = FALSE)

similarly based on p value also the same evidence.

there is significant evidence that the proportion of those who divorce is higher for those having children early.

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