Question

According to official census figures, 8% of couples living together are not married. A researcher took a random sample of 400 couples and found that 38 of them are not married. Test if the current percentage of unmarried couples is different from 8%.

Answer 1

H₀: P = 0.08

H₁: P = 0.08

= 38/400 = 0.095

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                             = (0.095 - 0.08)/sqrt(0.08 * (1 - 0.08)/400)

                             = 1.11

For alpha = 0.05, the critical values are z_0.025 = +/- 1.96

As the test statistic value is not greater than the upper critical value (1.11 < 1.96), so we should not reject the null hypothesis.

So there is not sufficient evidence to conclude that the current percentage of unmarried couples is different from 8%.