Question

In a recent survey of 45 apartment residents, 28 had phone answering machines. In a survey of 55 homeowners, 20 had phone answering machines. Can it be concluded that there is no difference in proportions of people who have phone answering machines in the two groups? Use α = .05.

What is the null hypothesis?

What is the alternative hypothesis?

The claim is the null hypothesis. True or False?

This test is: Right- tailed, left- tailed, or two- tailed?

What is the critical value?

What is the test value?

After comparing the test value to the critical value(s) we: reject the null hypothesis or do not reject the null hypothesis?

Is there or is there not enough evidence to support or reject the claim?

Answer 1

Solution:

1)

What is the null hypothesis?

H₀ :

2)

What is the alternative hypothesis?

H₁:

3)

The claim is the null hypothesis. True or False?

TRUE

4)

This test is: Right- tailed, left- tailed, or two- tailed?

two- tailed

5)

α = .05.

α/2 = 0.025

Critical values are   

i.e. -1.96 , 1.96

6)

What is the test value?

Given that,

n₁ = 45

x₁ = 28

₁ = 0.6222

n₂ =50

x₂ = 20

₂ = 0.3636

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = 0.48

1 - = 1 - 0.48 = 0.52

The test statistic z is

z =

   = 2.57

7)

2.57 > 1.96

So ,

reject the null hypothesis

8)

There is enough evidence to reject the claim