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).

The given data is

The null hypothesis states that there is no association between the variables:

$H_0$: There is no association between the variables

(type of degree and favoring death penalty)

The alternative hypothesis states that there is an association between the variables:

$H_a$: There is an association between the variables

(type of degree and favoring death penalty)

The p-value is given as

$P=0.000=0.0\%$

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme if the null hypothesis is true.

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

$H_0$: There is no association between the variables

$H_a$: There is an association between the variables.

The given data is

Find the hypothesis

$H_0:p_1-p_2=0$

$H_0:p_1-p_2\ne 0$

The P- value is

$P=0.000=0.0\%$

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.