Chapter 12.2, Problem 20E

Are you an optimist? The General Social Survey asked 1373 men and 993 women m the United

States Whether they agreed that they were generally optimistic about the future. The results are presented in the following table.

1. Compute the value of the 72 statistic for testing the hypothesis that the opinion on optimism is independent of gender.
2. Compute the proportion of men who were optimistic.
3. Compute the proportion of women who were optimistic.
4. Compute the test statistic z for testing the null hypothesis that the two proportions are equal versus the alternative that they are not equal.
5. Show that $x^2=z^2.$
6. Use technology to find the P-value for each test. Show that the P-values are equal.
7. Conclude that when a contingency table has two rows and two columns, the chi-square test is equivalent to the test for the difference between proportions.