Question

according to official censes figures,8% of couples living together are not arried.A researcher took a random sample of 400 couples and found that 9.5% of them are not married.Test at the 15% significanve level if the current percentage of unmarried couples is different from 8%

Answer 1

$H_0:\pi=0.08.$

$H_a:\pi\ne0.08.$

Tests statistic: $z=\frac{0.095-0.08}{\sqrt{\frac{0.08(1-0.08)}{400}}}=1.11.$

P-value: $p=2P(Z>1.11)=0.2670.$

Since the p-value is greater than 0.15, fail to reject the null hypothesis.

There is no sufficient evidence that the current percentage of unmarried couples is different from 8%.