Question

A humane society claims that 5% of U.S. households have taken in a stray dog. In a random sample of 200 U.S. households, 12 say they have taken in a stray dog. At α = 0.05, is there enough evidence to reject the society’s claim?

Answer 1

Solution:

Sample size n = 200

x = 12

= 12/200 = 0.06

Claim: p = 5% = 0.05

Use  0.05 level of significance

1)

H0: p= 0.05

Ha: p    0.05

2)

The test statistic z is

z =  

=  (0.06- 0.05)/[00.5*(1 - 0.05)/200]

= 0.65

3)

Two tailed test

So ,

p value = P(Z < -z) + P(Z > +z) = P(Z < -0.65)+P(Z > 0.65) = 0.2578+0.2578 =0.5156

p value = 0.5156

4)

Fail to reject H0

(Because p value is greater than level of significance)

5)

There is not sufficient evidence to reject the claim that 5% of U.S. households have taken in a stray dog.