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

Jayce Dougherty · Accepted Answer

Final Answer : B, Explanation :  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 1.645n = 200 (sample size)Plugging in the values, we get:CI = 0.4 ± 1.645*√(0.4(1-0.4)/200)= 0.4 ± 0.057Therefore, 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.

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