Question

Experts claim that 5% of crimes are committed by women. Is there enough evidence to reject the claim if in a sample of 50 crimes, 5 were committed by women? Use 5% significant level.

Answer 1

$H_0 : p = 0.05 \\ H_1 : p ≠ 0.05$

Critical value at 0.05 level = -1.96, 1.96

Rejection region = reject H₀ if z < -1.96 or z >1.96

Sample proportion

$\hat{p} = \frac{5}{50} = 0.1$

Test statistics

$z = \frac{\hat{p}-p}{\sqrt{p(1-p)/n}} \\ = \frac{0.1-0.05}{\sqrt{0.05(1-0.05)/50}} \\ = 1.62$

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H₀.

We conclude at 0.05 level that we fail to support the claim.