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 140 men, and 40% own cats.

You sample 120 women, and 25% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

Solution :

Given that,

n₁ = 140

Point estimate = sample proportion = ₁ = 0.40

n₂ = 120

Point estimate = sample proportion = ₂ = 0.25

The value of the pooled proportion is computed as,

= ( x₁ + x₂ ) / ( n₁ + n₂ )

= (56 + 30 ) / (140 + 120 )

= 0.331

1 - = 0.669

Test statistics

z = (₁ - ₂ ) / *(1-) ( 1/n₁ + 1/n₂ )

= ( 0.40 - 0.25) / ( 0.331 * 0.669) (1/140 + 1/120 )

= 2.56