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 160 men, and 25% own cats. you sample 120 women, and 20% own cats. find the test statistic, rounded to two decimal places.

Given:You sample 160 men, and 25% own cats

          You sample 120 women, and 20% own cats.

To Find : Find the test statistic, rounded to two decimal places.

Solution:

You sample 160 men, and 25% own cats.

No. of men have cats =

                                    =

So,

You sample 120 women, and 20% own cats.

No. of women have cats =

                                    =

So,

We will use Comparing Two Proportions

Let and be the probabilities of men having cat and women having cat receptively

Formula of test statistic :

Substitute the values  

test statistic :

test statistic :

So, test statistic is 0.986

a = 11 : 4

b = 38

c = 1 for every 6