Question

In: Statistics and Probability

In the 2008 General Social Survey, incomes of married respondents were classified as above average, average,...

  1. In the 2008 General Social Survey, incomes of married respondents were classified as above average, average, and below average. Respondents also answered a question about marital happiness as not happy, pretty happy, or very happy. The results are below:

Marital Happiness

Income

Not Happy

Pretty Happy

Very Happy

Totals

Above Average

123

105

7

235

Average

291

151

17

459

Below Average

172

83

6

261

Totals

586

339

30

955

Conduct an appropriate test to determine whether or not there is a statistically significant association between marital happiness and income at the 5% significance level.

  1. Which is the independent variable and which is the dependent variable?
  2. For individuals with average income, what percentage of individuals report their marital happiness as “pretty happy?”
  3. Are the basic assumptions of the hypothesis test satisfied?
  4. What are the null and alternative hypotheses?
  5. Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?
  6. Calculate the appropriate test statistic, showing all your work. You should explicitly display (1) expected values for each cell and (2) the test statistic contribution of each cell in addition to calculating the overall test statistic.
  7. Calculate the corresponding p-value from the appropriate table or online calculator.
  8. What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Solutions

Expert Solution

(A) Marital happiness is depend on the income, therefore marital happiness is the dependent variable and income is independent variable for this problem.

(B) The percentage of individual reports their marital happiness as pretty happy with average income = 151/459 = 0.3290 = 32.90%

(C) Yes, the basic assumptions of the hypothesis test are fulfilled i. e.

Two or more categories for each variable

Observations should be independent

Sample size should be large

Expected frequency for each cell should be at least one

(D) The hypothesis of the test are

H0: There is no association between income and marital happiness

Ha: There is statistically significant association between income and marital happiness.

After performing the chi square test, we found the test statistic is 12.8369 and the P-value of the test is 0.012, which is less than the level of significance alpha 0.05, therefore we reject the null hypothesis and concluded that there is statistically significant association between income and marital happiness.

Note: I am bounded to answer the question according to guidelines, therefore I can solve only four parts of the question.

Thank you.


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