In an opinion survey a random sample of 1000 adults from the

In an opinion survey, a random sample of 1000 adults from the U.S.A and 1000 adults from Germany were asked whether they supported the death penalty. 590 American adults and 560 German adults indicated that they supported the death penalty. The researcher wants to know if there is sufficient evidence to conclude that the proportion of adults who support the death penalty is higher in the U.S.A. than in Germany. What is the decision at a =.05 and 0.10

Solution

Ho: p1=p2

Ha: p1>p2

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.59-0.56)/sqrt(0.59*(1-0.59)/1000+0.56*(1-0.56)/1000)

=1.36

Given a=0.05, the critical value is Z(0.05)=1.645

a=0.1, the critical value is Z(0.1)=1.25

Since Z=1.36 is less than 1.645, we do not reject Ho at a=0.05.

Since Z=1.36 is larger than 1.25, we reject Ho at a=0.1