Testing the Difference between Two Proportions

 In testing the difference between two proportions, we use the z-test to compare the two proportions. And in order to use the z-test, the samples must be independent to each other and n₁p₁ ≥ 30;n₂p₂ ≥ 30, n₁q₁ ≥ 30;n₂q₂ ≥ 30. 

This is the Formula for the z-test for Comparing Two Proportions.
              z=(p̂1-p̂2)-(p1-p2)/√(p-bar x q-bar x (1/n1+1/n2))

Let me give you an example

In a sample of 60 residents of Brgy. Mapurok, 9 had their own washing machine. In a sample of 70 resident of Brgy. Marupok, 24 had their ow2n washing machine. at a=0.05,can it be concluded that their is a significant difference in the proportion of the two Barangays which owns a washing machine?

Solution:
p̂1=9/60=0.15
p̂2=24/70=0.34
p-bar= 9+24/60+70=0.25
q-bar=1-0.25=0.75

Step 1: State the Hypothesis
             Ho:p1=p2
             H1:p1≠p2

Step 2: Find the Critical Value
          a=0.05,two tailed test, C.V=± 1.96

Step 3: Find the Test Value
              z= (p̂1-p̂2)-(p1-p2)/√(p-bar x q-bar x (1/n1+1/n2))
             = (0.15-0.34)/ √(0.25)(0.75)(1/60+1/70)= -2.49

Step 4:Make the decision
          Reject the null hypothesis

Step 5: Summarize the results
          There is enough evidence to support the claim



By: Dustin Joshua A. Esquia III-Gold