Find the test statistic

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 120 men, and 65% own cats.

You sample 60 women, and 55% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

test statistic is z = (p1 - p2)/sqrt(p(1-p)/n1 + p(1-p)/n2)

where p1 = 0.65, n1 = 120

p2 = 0.55, n2 = 60

x1 = number of successes men = 120 * 0.65 = 78

x2 = number of successes women = 60 * 0.55 = 33

p = pooled proportion = (x1 + x2)/(n1 + n2) = 111/180 = 0.62