Question

A labor union spokesman claims that 75% of union members will support a strike if their basic demands are not met. A company spokesman believes the true percentage is higher and runs a hypothesis testing at 10% significance level. (a) Compute the test statistic if 100 of 125 union members say they will strike.

Answer 1

$H_0: p = 0.75 \\ H_1: p <0.75 \\ \hat{p} = \frac{100}{125} = 0.8$

(a) Test-statistic

$Z = \frac{\hat{p} – p}{\sqrt{\frac{pq}{n}}} \\ = \frac{0.8-0.75}{\sqrt{\frac{0.75 \times 0.25}{125}}} \\ = \frac{0.05}{0.03873} \\ = 1.29$