Elementary Statistics and Computer Application

Test for equality of two proportions

Given two sets of sample data of large size n1 and n2 from attributes. We may examine whether the two samples come from the populations having the same proportion. We may proceed as follows:
1. Null Hypothesis (Ho):

• Ho: The given two sample would have come from a population having the same proportion P1=P2
2. Alternative Hypothesis (H1)

• H1 : The given two sample may not be from a population with specified proportion
• P1≠P2 (Two Sided)
  P1>P2(One sided-right sided)
  P1<P2(One sided-left sided)
3. Test statistic

When P1and P2 are not known, then
for heterogeneous population
Where q1 = 1-p1 and q2 = 1-p2
for homogeneous population
p= combined or pooled estimate.

4. Level of Significance

• The level may be fixed at either 5% or 1%
5. Expected vale

• The expected value is given by


6. Inference

• If the observed value of the test statistic Z exceeds the table value Ze we may reject the Null Hypothesis Ho otherwise accept it.