Answer to Question #290173 in Statistics and Probability for Rod

Question

A labor union claims “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available” 74 persons out of the 200 sampled said they would return to work. Can we conclude that the proportion returning to work is different from (either above or below) 0.40?

Required: Test the hypothesis with 2% significance level.

Answer 1

Null hypothesis $H_0:\pi=0.40.$

Alternative hypothesis $H_a:\pi\ne0.40.$

Test statistic: $z=\frac{\hat p-\pi}{\sqrt{\frac{\pi(1-\pi)}{n}}}=\frac{\frac{74}{200}-0.40}{\sqrt{\frac{0.40(1-0.40)}{200}}}=-0.87.$

P-value: $p=2P(Z<-0.87)=0.3865.$

Since the p-value is greater than 0.02, fail to reject the null hypothesis.

There is no sufficient evidence to conclude that the proportion returning to work is different from 0.40.