Consider the following competing hypotheses and accompanying sample data. Use Ta

Question

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 10% significance level, calculate the critical value. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

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

Explanation / Answer

Null, Ho: p1 >= p2
Alternate, H1: p1 < p2
Test Statistic
Sample 1 : X1 =223, n1 =418, P1= X1/n1=0.533
Sample 2 : X2 =245, n2 =418, P2= X2/n2=0.586
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.56
Q^ Value For Proportion= 1-P^=0.44
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.533-0.586)/Sqrt((0.56*0.44(1/418+1/418))
Zo =-1.533
| Zo | =1.533
Critical Value
The Value of |Z | at LOS 0.1% is 1.282
We got |Zo| =1.533 & | Z | =1.282
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail - Ha : ( P < -1.5328 ) = 0.06267
Hence Value of P0.1 > 0.06267,Here we Reject Ho

[ANSWERS]
Test statistic:-1.533
Crtical value : 1.282
Reject H0 since the value of the test statistic is not less than the critical value

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