Question

One-child families ~ The one-child policy was introduced in China in 1979 by the Chinese government. This policy set a limit on the number of births each Chinese couple could have. A research group randomly chose 305 Chinese couples and found 160 of them with only one child. Among 448 American couples the group studied, 96 couples gave birth to only one child.

The research group wants to estimate the actual difference between the proportions of Chinese and American couples who have only one child.

Notation: 1=Chinese and 2=American.

Based on this data, what is the upper bound for a 95% confidence interval for the difference in the population proportions, p1-p2?

Answer 1

Here, , n1 = 305 , n2 = 448
p1cap = 0.5246 , p2cap = 0.2143

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.5246 * (1-0.5246)/305 + 0.2143*(1-0.2143)/448)
SE = 0.0345

For 0.95 CI, z-value = 1.96

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.5246 - 0.2143 - 1.96*0.0345, 0.5246 - 0.2143 + 1.96*0.0345)
CI = (0.2427 , 0.3779)

upper bound = 0.3779