a. Convert the frequency responses to percentages by calculating the percentage of each column total falling in each row. Also, convert the row totals to percentages of the total number of responses. Display the percentages in a table.
b. Create a bar graph with row 1 percentage on the vertical axis and column number on the horizontal axis. Show the row 1 total percentage as a horizontal line on the graph.
c. What pattern do you expect to see if the rows and columns are independent? Does the plot support the result of the test of independence in Exercise 8.55?
Consider the following 2 × 3 (i.e., r = 2 and c = 3 ) contingency table:
Column | ||||
|
| 1 | 2 | 3 |
Row | 1 | 9 | 34 | 53 |
| 2 | 16 | 30 | 25 |
a. Specify the null and alternative hypotheses that should be used in testing the independence of the row and column classifications.
b. Specify the test statistic and the rejection region that should be used in conducting the hypothesis test of part a . Use α = .01.
c. Assuming that the row classification and the column classification are independent, find estimates for the expected cell counts.
d. Conduct the hypothesis test of part a. Interpret your result.
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