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): n_1 = 82, x_1 = 57 Fourth-Years (Pop. 2): n_2 = 80, X_2 = 53 Is there evidence, at an alpha = 0.03 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. The value of the standardized test statistic: The p-value is Your decision for the hypothesis test: Reject H_0. Do Not Reject H_0. Do Not Reject H_1. Reject H_1.

Explanation / Answer

Null, There Is No Significance between them Ho: p1 = p2
Alternate, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =57, n1 =82, P1= X1/n1=0.695
Sample 2 : X2 =53, n2 =80, P2= X2/n2=0.663
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.679
Q^ Value For Proportion= 1-P^=0.321
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.695-0.663)/Sqrt((0.679*0.321(1/82+1/80))
Zo =0.445
| Zo | =0.445
Critical Value
The Value of |Z | at LOS 0.03% is 2.17
We got |Zo| =0.445 & | Z | =2.17
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 0.4447 ) = 0.6566
Hence Value of P0.03 < 0.6566,Here We Do not Reject Ho

[ANSWERS]
a. Zo =0.445
b. P_value = 0.6566
c. Do not Reject Ho

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