10.31

Using the given sample information, test the following hypotheses.

Sample 1	Sample 2
n1 = 368	n2 = 405
x1 = 175	x2 = 182

1. H₀: p₁ – p₂ = 0
   H_a: p₁ – p₂ ≠ 0
   
   
   
   

Sample 1	Sample 2
n1 = 649	n2 = 558

Let α = .05

2. H₀: p₁ – p₂ = 0
   H_a: p₁ – p₂ > 0
   Let α = .10

(a)

Use the following formula:

 

 

 

 

 

α = .05. α/2 = .025 as this is a two-tailed test.

 

 

If the observed value of Z is greater than +1.96 or less than -1.96, the decision will be to reject the null hypothesis.

 

 

 

 

 

 

 

Z is in the non-rejection region, therefore we fail to reject.