In preparation for contract renewal negotiations, the United Auto Workers survey
ID: 3160378 • Letter: I
Question
In preparation for contract renewal negotiations, the United Auto Workers surveyed its members to see whether they preferred a large increase in retirement benefit or a smaller increase in salary. In a group of 1000 male members who were polled, 743 were in favor of increased retirement benefit. Of 500 female members, 405 favored the increase in retirement benefit. Use the .05 level of significance to test the hypothesis that equal proportions of men and women are in favor of increased retirement benefits.
A. Since critical z value is -1.645, we have to reject the null hypothesis and conclude that the proportions of male and female who favor the increase in retirement benefit are significantly different.
B. Since critical z value is +1.96, we have to reject the null hypothesis and conclude that the proportions of male and female who favor the increase in retirement benefit are significantly different.
C. Since critical z value is +1.96, we have to reject the null hypothesis and conclude that the proportions of male and female who favor the increase in retirement benefit are not significantly different.
D. Since critical z value is -1.645, we have to reject the null hypothesis and conclude that the proportions of male and female who favor the increase in retirement benefit are not significantly different.
Explanation / Answer
Null,equal proportions of men and women are in favor of increased retirement benefits Ho: p1 = p2
Alternate, not Ho H1: p1 != p2
Test Statistic
Sample 1 : X1 =743, n1 =1000, P1= X1/n1=0.743
Sample 2 : X2 =405, n2 =500, P2= X2/n2=0.81
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.765
Q^ Value For Proportion= 1-P^=0.235
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.743-0.81)/Sqrt((0.765*0.235(1/1000+1/500))
Zo =-2.886
| Zo | =2.886
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.886 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -2.8864 ) = 0.0039
Hence Value of P0.05 > 0.0039,Here we Reject Ho
B. Since critical z value is +1.96, we have to reject the null hypothesis and conclude that the proportions of male and female who favor the increase in retirement benefit are significantly different.