Question

In this exercise, a two-way table is shown for two groups, 1 and 2, and two possible outcomes, A and B.

(a) What proportion of all cases had Outcome A?
(b) What proportion of all cases are in Group 1?
(c) What proportion of cases in Group 1 had Outcome B?
(d) What proportion of cases who had Outcome A were in Group 2?"

Answer 1

The question involves using a contingency table to calculate different probabilities, including the proportion of cases with a specific outcome and the proportion of cases belonging to certain groups.

Step-by-step explanation:

The student's question involves understanding how to work with contingency tables to determine various probabilities related to multiple dependent variables. To answer parts (a) through (d), we need to calculate different types of probabilities such as marginal and conditional distributions based on the information given in the two-way table.

• To find the proportion of all cases with Outcome A, one would add the number of cases in both groups that had Outcome A and divide by the total number of cases.
• To find the proportion of cases in Group 1, one would divide the total number of cases in Group 1 by the overall total number of cases.
• To calculate the proportion of cases in Group 1 with Outcome B, one would divide the number of cases in Group 1 with Outcome B by the total number of cases in Group 1.
• Lastly, to find the proportion of cases with Outcome A that were in Group 2, one would divide the number of cases with Outcome A in Group 2 by the total number of cases with Outcome A.

These calculations utilize marginal and conditional distributions mentioned in the provided text snippet from the study material.