Question

A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a simple random sample of 200 couples who had children within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. Let p = the population proportion of couples who had children within the first two years of marriage and are divorced within five years. A newspaper reported that a third of all couples who had children within the first two years of marriage get divorced within five years. The sociologist wants to test this claim at 10% significance level.

a) Formulate the null and alternative hypothesis

b) Calculate an appropriate test statistic. Show your calculation and from what distribution this statistic is computed (i.e. z, t, F, etc).

c) Determine the P-value. Write what function you use to get the P-value. Do not simply write the P-value (i.e. normcdf, tcdf, Fcdf, chi-square, etc)

d) Write your conclusion (with context). Do not write simply “Reject” or “Do Not reject”

I am very confused about where to start. Thank you for your help, it helps me a lot.

Answer 1

a) H0: the population proportion of couples who had children within the first two years of marriage and are divorced within five years is one third

i.e. H0: P = 1/3

H0: the population proportion of couples who had children within the first two years of marriage and are divorced within five years is not one third

i.e. H0: P not = 1/3

b) Test Statistic:

Sample proportion Pbar = 80/200 = 0.4

c)

d) Since P-value is 0.0454 < 0.05 so we reject H0

Thus we conclude that the population proportion of couples who had children within the first two years of marriage and are divorced within five years is not one third

i.e. P is not = 1/3.