Chapter 11.2, Problem 11PB

Marital happiness and income In Exercise 11.5 when you used the GSS to download a 3 × 3 table for family income and marital happiness in 2012, you should have obtained results similar to the following table.

1. a. State the null and alternative hypotheses for the test.
2. b. What is the number of degrees of freedom for the chisquared test?
3. c. The chi-squared statistic for the table equals X² = 4.58. (i) What value do you expect for X² if the null hypothesis were true? (ii) How many standard deviations is 4.58 from this expected value? (Hint: The standard deviation of the chi-squared distribution equals $\sqrt{2\times df}$). (iii) Is X² = 4.58 an extreme value? Explain.
4. d. How large an X² value would give a P-value of exactly 0.05?
5. e. Find (at least approximately, using Table C in the appendix) the P-value and give a conclusion for the test in context.
6. f. Verify that the expected cell count in the first cell equals 4.84. Could this be a problem? Explain.