Question

You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats.

You sample 110 men, and 103 own cats.

You sample 50 women, and 15 own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

Proportions are represented by p₁ (men) and p₂ (women).
p₁=103/110=0.9364, p₂=15/50=0.3.
p=(103+15)/(110+50)=118/160=59/80=0.7375.
SE=√(0.7375×0.2625(1/110+1/50))=0.075 approx.
Z=(0.9364-0.3000)/0.075=8.48 approx.
Test statistic=8.48.