Consider the following competing hypotheses and accompanying

Consider the following competing hypotheses and accompanying sample data. Use Table 1.

Calculate the value of the test statistic. (Negative values should be indicated by a minus sign.Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

At the 5% significance level, calculate the critical value. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Solution

Null Hypothesis, Ho: p1 - p2 >=0
Alternate Hypothesis, H1: p1 - p2 <0
Test Statistic
Sample 1 : X1 =224, n1 =386, P1= X1/n1=0.58
Sample 2 : X2 =245, n2 =386, P2= X2/n2=0.635
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.608
Q^ Value For Proportion= 1-P^=0.392
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.58-0.635)/Sqrt((0.608*0.392(1/386+1/386))
Zo =-1.548
| Zo | =1.55
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.548 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -1.5478 ) = 0.06083
Hence Value of P0.05 < 0.06083,Here We Do not Reject Ho

a) Zo =-1.55
b) The Value of |Z | at LOS 0.05% is -1.645
c) Do not reject H0 since the value of the test statistic is less than the critical value.