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 45% own cats. You sample 120 women, and 35% own cats. Find the test statistic, rounded to two decimal places. Find the test statistic, rounded to two decimal places.

Answer 1

Test statistic =1.30

Explanation:

Given that you are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats.

Men Women Difference

Sample size n 60 120

Proportion p_1, p_2 0.45 0.35 0.10

60 120 180

0.45 0.35 0.383333333

27 42 69

p = 0.3833

Std error for proportion difference =
`\bar p (1-\bar p)((1)/(n_1)+(1)/(n_2))\\=0.3833(0.6167)((1)/(60)+(1)/(120))\\=0.0769`

Test statistic =
`(p_1-p_2)/(\bar p (1-\bar p)((1)/(n_1)+(1)/(n_2))  )`

=
`1.3008`

=1.30