Question

According to official census figures, 8% of couples living together are not married. A researcher took a

random sample of 400 couples in a large metropolitan city and found that 38 of them are not married. Estimate the proportion of unmarried couples in this city with 99.5% confidence.

Answer 1

$\hat p=\frac{38}{400}=0.095.$

$99.5\%CI=(0.095-2.807\sqrt{\frac{0.095(1-0.095)}{400}},0.095+2.807\sqrt{\frac{0.095(1-0.095)}{400}})=$

$=(0.04676,0.1432).$

We are 99.5% confident that the proportion of unmarried couples in this city lies between 4.676% and 14.32%.