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 = .10?
A)Reject the null hypothesis
B)Can't reject the null hypothesis

Question

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  = .10?
A)Reject the null hypothesis 
B)Can't reject the null hypothesis

Quizplus · Accepted Answer

To determine 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, we need to conduct a hypothesis test. Let p1 be the proportion of adults in the U.S.A. who support the death penalty and p2 be the proportion of adults in Germany who support the death penalty. The null hypothesis is H0: p1<=p2 and the alternative hypothesis is Ha: p1>p2.

We can use the z-test for two proportions to test the hypothesis. The test statistic is calculated as Z = (p1-p2) / sqrt(p(1-p)(1/n1+1/n2)), where p = (x1+x2)/(n1+n2), x1 and x2 are the number of adults who support the death penalty in the U.S.A. and Germany, respectively. n1 and n2 are the sample sizes.

Plugging in the values, we get Z = (0.59-0.56) / sqrt(0.57*0.43*(1/1000+1/1000)) = 1.20 (rounded to two decimal places)

At 10% level of significance, the critical value of Z for a one-tailed test is 1.28. Since the calculated value of Z (1.20) is less than the critical value, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is sufficient evidence to support the claim that the proportion of adults who support the death penalty is higher in the U.S.A. than in Germany at the 10% level of significance.

In an Opinion Survey,a Random Sample of 1000 Adults from the U.S.A