11.11 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.

a. State the null and alternative hypotheses for the test.

b. What is the number of degrees of freedom for the chisquared test?

c. The chi-squared statistic for the table equals X2 = 4.58.
(i) What value do you expect for X 2 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 12 * df ). (iii) Is X2 = 4.58 an extreme value? Explain.

d. How large an X2 value would give a P-value of exactly 0.05?

e. Find (at least approximately, using Table C in the appendix) the P-value and give a conclusion for the test in context.

f. Verify that the expected cell count in the first cell equals 4.84. Could this be a problem? Explain.

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Income Not Marital Happiness Pretty Very Above 6. 62 139 Average 7 125 283 Below 6 69 115