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 60 men, and 60% own cats.

You sample 140 women, and 40% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

Solution :

Given that,

n₁ = 60

Point estimate = sample proportion = ₁ = 0.60

n₂ = 140

Point estimate = sample proportion = ₂ = 0.40

The value of the pooled proportion is computed as,

= (₁n₁ + ₂n₂ ) / ( n₁ + n₂ )

= (36 + 56 ) / (60 + 140 )

= 0.46

1 - = 0.54

Test statistics

z = (₁ - ₂ ) / *(1-) ( 1/n₁ + 1/n₂ )

= (0.60 - 0.40 ) / ( 0.46 * 0.54) (1/60 + 1/140 )

= 2.60