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 20% own cats.

You sample 80 women, and 35% own cats.

Find the test statistic, rounded to two decimal places.

Answer 1

Here, we want to test:

H₀ : proportion of men who own cat is same as the proportion of women who own cat. i.e. =0 v/s

H1 : proportion of men who own cat is different from the proportion of women who own cat. i.e.

When and denote the population porportion of men and women who own cat respectively.

sample proportion of men who own cats = =0.2

sample size = n₁= 160

sample proportion of women who own cats = =0.35

sample size = n₂= 80

The test statistic Z is given by,

where

  

ANS: The required value of the test statistic is -2.53