A sociologist is studying the effect of having children within the first 2 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 2 years of marriage.Following up on these couples,she finds that 80 couples are divorced within 5 years.Let p = the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years.What is a 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years?
A)0.402 ± 0.035
B)0.402 ± 0.057
C)0.402 ± 0.067
D)0.402 ± 0.088

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we can use the following formula:

CI = p̂ ± z*√(p̂(1-p̂)/n)

where:

p̂ = 80/200 = 0.4 (sample proportion)
z* = the z-score corresponding to a 90% confidence level, which is 1.645
n = 200 (sample size)

Plugging in the values, we get:

CI = 0.4 ± 1.645*√(0.4(1-0.4)/200)
   = 0.4 ± 0.057

Therefore, the 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years is 0.402 ± 0.057. The best choice is B.

A Sociologist Is Studying the Effect of Having Children Within