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
|
|
Total
|
200
|
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.