Compare 2 Population Proportions

Compare 2 Population Proportions

1. Hypothesis Test

   • H0: p1 -p2 = p0
     • Ha: p1 - p2 < p0
       • Ha: p1 - p2 > p0
         • Ha: p1 - p2 != p0
           • 2-tail
         • Upper Tail
       • Lower Tail

2. Calculate Test Statistic

   • Z-Obs
   • Convert the sampling distribution of p1 - p2 to the Z-dist
     • CASE #1: H0: p1 - p2 != 0
     • CASE #2 : H0:: p1 - p2 = 0

3. Determine P - value

   • P (Z > Zobs)
     • Area tp RIGHT of test stat
   • P (Z < Zobs)
     • Area to LEFT of Test Stat
   • P ( Z > |Zobs| ) x 2
     • Area to RIGHT of abs of test stat, multiply by 2
   • Make Decision
     • P < alpha || REJECT H0
     • P > alpha || Fail to Reject.
     • Make Conclusion
       • Based on alternative hypothesis, and p value compared to alpha. Either reject, or fail to reject the null

4. Independent Random Samples