Question

 Experts claim that 10% of murders are committed by women. Is there enough evidence to reject the claim if in a sample of 67 murders, 10 were committed by women? At , test the hypothesis using the p-value method

Answer 1

$H_0:p=0.1.$

$H_a:p\ne0.1.$

Test statistic: $z=\frac{\frac{10}{67}-0.1}{\sqrt{\frac{0.1(1-0.1)}{67}}}=1.34.$

P-value: $p=2P(Z>1.34)=0.1802.$

Since the p-value is greater than 0.05, fail to reject the null hypothesis.

There is not enough evidence to reject the claim that 10% of murders are committed by women.