sample Test Statistic

Question

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

You sample 100 men, and 80% own cats.

You sample 200 women, and 75% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

x1 = 100 * 0.8 = 80

x2 = 200 * 0.75 = 150

n1 = 100

n2 = 200

pooled proportion p = (x1 + x2)/(n1 + n2) = (80 + 150)/300 = 0.76

p1 = 0.8

p2 = 0.75

z = (p1 - p2)/sqrt(p * (1-p) * (1/n1 + 1/n2))

= (0.8 - 0.75)/sqrt(0.76 * 0.25 * (1/100 + 1/200))