Question

You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats. You sample 70 men, and 30% own cats. You sample 170 women, and 10% own cats. Find the proportion of the pooled samples, (p sub c), as a decimal, rounded to two decimal places.

Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. Then find the critical value, test statistic, and do we reject or decline to reject the null?

Answer 1

Let p1 be the proportion for men

Let p2 be the proportion for women

Ho: p1=p2 (i.e. null hypothesis)

Ha: p1<p2 (i.e. alternative hypothesis)

pooled sample =p^

finding a p^ value for proportion p^=(p1*n1 + p2*n2) / (n1+n2)
p^=0.158
q^ Value For Proportion= 1-p^=0.842

The test statistic is

we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
Z =(0.3-0.1)/sqrt((0.158*0.842(1/70+1/170))
Z =3.858

It is a one-tailed test.

Given a=0.1, the critical value is Z(0.1) =-1.28 (from standard normal table)

Since Z=3.85 is greater than -1.28, we Fail to reject the null hypothesis