Consider the following competing hypotheses and accompanying

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

At the 1% significance level, find the critical value(s). (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

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

H0: 0

HA: < 0

Solution

Null, Ho: p1 - p2 >= 0
Alternate, H1: p1 - p2 < 0
Test Statistic
Sample 1 : X1 =242, n1 =412, P1= X1/n1=0.5874
Sample 2 : X2 =252, n2 =412, P2= X2/n2=0.6117
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.5995
Q^ Value For Proportion= 1-P^=0.4005
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.587-0.6117)/Sqrt((0.6*0.4005(1/412+1/412))
Zo =-0.711
| Zo | =0.711
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo| =0.711 & | Z | =2.326
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail - Ha : ( P < -0.711 ) = 0.23856
Hence Value of P0.01 < 0.23856,Here We Do not Reject Ho

ANSWER:
a)
Critical Value, |Z | at LOS 0.01% is -2.326
b)
Zo =-0.71
c)
Do not reject H0 since the value of the test statistic is less than the critical value.