Two groups were polled about their attitudes towards capital punishment. In one group 30 out of 100 favored capital punishment, and in the other group 40 out of 80 favored
Capital punishment. Calculate an appropriate test value test the hypothesis that the
Population proportions are the same.
A) -37.40
B) -2.73
C) -0.20
D) -13.68

Question

Quizplus · Accepted Answer

The appropriate test for comparing two proportions is the z-test for two proportions. The formula for the z-test statistic in this context is:$$ z = \frac{p_1 - p_2}{\sqrt{P(1-P)(\frac{1}{n_1} + \frac{1}{n_2})}} $$where $p_1$ and $p_2$ are the sample proportions (0.3 and 0.5, respectively), $n_1$ and $n_2$ are the sample sizes (100 and 80, respectively), and $P$ is the pooled proportion $\frac{30+40}{100+80} = \frac{70}{180}$.Plugging the values into the formula gives a z-value of approximately -2.73, which is the correct test value for comparing the two proportions.

Two Groups Were Polled About Their Attitudes Towards Capital Punishment