(1 pt) Two random samples are taken, one from among first-year UVA students and

Question

(1 pt) 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=87, x1=60

Fourth-Years (Pop. 2): n2=89, x2=61   

Is there evidence, at an =0.08 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. Do Not Reject H1.

B. Reject H0.

C. Reject H1.

D. Do Not Reject H0.

Explanation / Answer

Null, Ho: p1 = p2
Alternate, H1: p1 != p2
Test Statistic
Sample 1 : X1 =60, n1 =87, P1= X1/n1=0.69
Sample 2 : X2 =61, n2 =89, P2= X2/n2=0.685
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.688
Q^ Value For Proportion= 1-P^=0.313
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.69-0.685)/Sqrt((0.688*0.313(1/87+1/89))
Zo =0.061
| Zo | =0.061
Critical Value
The Value of |Z | at LOS 0.08% is 1.751
We got |Zo| =0.061 & | Z | =1.751
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 0.061 ) = 0.9514
Hence Value of P0.08 < 0.9514,Here We Do not Reject Ho

[ANSWERS]
1. Zo =0.061
2. P-value = 0.95142
3. D. Do Not Reject H0.

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