Proportion Comparison with Independent Samples of n1 n2 30

Proportion Comparison with Independent Samples of n1 & n2 30 We have two independent samples with sizes and sample proportions as follows: n1 = 145 p1 = 0.43 n2 = 136 p2 = 0.47 a) Are the conditions for normality approximation met? Explain. b) Test H0: 1 2 versus H1: 1 < 2 at the 0.01 level of significance. c) Determine the pvalue for the test. Hint: Round off probabilities and values to 5 decimal places. Determine probabilities based on some Excel probability and value lookups:

Solution

Set up Hypothesis
Null, Ho: p1 >= p2
Alternate, H1: p1 < p2
Test Statistic
Sample 1 : X1 =62.35, n1 =145, P1= X1/n1=0.43
Sample 2 : X2 =63.92, n2 =136, P2= X2/n2=0.47
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.449
Q^ Value For Proportion= 1-P^=0.551
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.43-0.47)/Sqrt((0.449*0.551(1/145+1/136))
Zo =-0.674
| Zo | =0.674
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo| =0.674 & | Z | =2.326
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -0.6736 ) = 0.25027
Hence Value of P0.01 < 0.25027,Here We Do not Reject Ho

[ANSWERS]
a)
P1 = 0.43>0.05, P2= 0.47>0.05, can normlizatoin be applicable

b) Zo =-0.674

c) P-Value: Left Tail - Ha : ( P < -0.6736 ) = 0.25027