The General Social Survey asked a random sample of adults, “Do you favour or oppose the death penalty for persons convicted of murder?” The following table gives the responses of people whose highest education was a high school degree and of people with a bachelor’s degree:
We can test the hypothesis of “no difference” in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.
(a) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw? Chi-Square Test: C1, C2 Expected counts are printed below-observed counts Chi-Square contributions are printed below expected counts
(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).

Question

Accepted Answer

(a) $H_{0}$ : There is no association between the variables

$H_{a}$ : There is an association between the variables

If there is no association between the variables, then we have a probability of $0.0 %$ of obtaining a similar or more extreme sample.

(b) We can deduce from this P-value that there is a difference between the population proportions, which is the case if the variables are related.

As a result, the two-sample z-test and the chi-square test are equivalent, as seen by the similar P-values.

Short Answer