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Question 1 - Comparison of conditional distributions. Consider the following 2 × 2 table:
Observed counts
Response variable
Explanatory variable
Total
1
2
Yes
70
90
160
No
130
110
240
200
400
(a) Compute the conditional distribution of the response variable for each of the two explanatory-variable categories.
(b) Display the distributions graphically.
(c) Write a short paragraph describing the two distributions and how they differ.
Question 2 - Expected cell counts and the chi-square test. Refer to Question 1. You decide to use the chi-square test to compare these two conditional distributions.
(a) What is the expected count for the first cell (observed count is 70)?
(b) Computer software gives you X2 = 4.17. What are the degrees of freedom for this statistic?
(c) Using Table F, give an appropriate bound on the P-value.
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