Two random samples are taken, one from among first-year UVA students and the oth

Question

Two random samples are taken, one from among first-year UVA students and the other from among fourth-year UVA students. Both samples are asked if they favor modifying the Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below:

First-Years (Pop. 1): n1=92, x1=49

Fourth-Years (Pop. 2): n2=92, x2=65

Is there evidence, at an =0.07 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The p-value is:

C. Your decision for the hypothesis test:

A. Reject H0.
B. Reject H1.
C. Do Not Reject H1.
D. Do Not Reject H0.

I got 2.4308 as my test statistic, which is wrong. Help is appreciated!

Explanation / Answer

Null, Ho: p1 = p2
Alternate, H1: p1 != p2
Test Statistic
Sample 1 : X1 =49, n1 =92, P1= X1/n1=0.533
Sample 2 : X2 =65, n2 =92, P2= X2/n2=0.707
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.62
Q^ Value For Proportion= 1-P^=0.38
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.533-0.707)/Sqrt((0.62*0.38(1/92+1/92))
Zo =-2.4296
| Zo | =2.4296
Critical Value
The Value of |Z | at LOS 0.07% is 1.812
We got |Zo| =2.4296 & | Z | =1.812
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -2.4296 ) = 0.0151
Hence Value of P0.07 > 0.0151,Here we Reject Ho

[ANSWERS]
1.Zo = -2.4296
2.P=0.0151
3. Reject H0.

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