Opinions about the death penalty The General Social Survey asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor 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:

Highest education level High school Bachelor’s degree Favor 1010 319 Oppose 369 185 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 twosample 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 Pvalue 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 C1 C2 Total 1 1010 319 1329 973.28 355.72 1.385 3.790 2 369 185 554 405.72 148.28 3.323 9.092 Total 1379 504 1883 Chi-Sq = 17.590, DF = 1, P-Value = 0.000

(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).

Test for Two Proportions Sample X N Sample p 1 1010 1379 0.732415 2 319 504 0.632937 Difference = p (1) − p (2)

Estimate for difference: 0.0994783 Test for difference = 0 (vs not = 0):

Z = 4.19 P-Value = 0.000