Question

You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats. You sample 160 men, and 50% own cats. You sample 140 women, and 25% own cats. Find the test statistic, rounded to two decimal places.

Answer 1

Pooled proportion = ( n1 * 1 + n2 * 2) / (n1 + n2)

= (160 * 0.50 + 140 * 0.25) / (160 + 140)

= 0.3833

Test statistics

z = (1 - 2) / sqrt [ ( 1 - ) * ( 1 / n1 + 1/n2) ]

= (0.50 - 0.25) / sqrt [ 0.3833 ( 1 - 0.3833) * ( 1 / 160 + 1 / 140) ]

= 4.44