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# Probability Topics: Practice 1: Contingency Tables (modified R. Bloom)

Module by: Roberta Bloom. E-mail the author

Summary: This module provides the opportunity for students to apply what they've learned about probability to solve a series of problems given a set of data. Students will practice constructing and interpreting contingency tables. This revision of the original module by S. Dean and Dr. B. Illowsky has been modified as follows: the data has been presented here in tabular form.

## Student Learning Objectives

• The student will practice constructing and interpreting contingency tables.

## Given

An article in the New England Journal of Medicine (by Haiman, Stram, Wilkens, Pike, et al., 1/26/06), reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most 10 cigarettes per day, there were 9886 African Americans, 2745 Native Hawaiians, 12,831 Latinos, 8378 Japanese Americans, and 7650 Whites. Of the people smoking 11-20 cigarettes per day, there were 6514 African Americans, 3062 Native Hawaiians, 4932 Latinos, 10,680 Japanese Americans, and 9877 Whites. Of the people smoking 21-30 cigarettes per day, there were 1671 African Americans, 1419 Native Hawaiians, 1406 Latinos, 4715 Japanese Americans, and 6062 Whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2305 Japanese Americans, and 3970 Whites.

## Complete the Table

Verify that the data above is entered into the table correctly.

Table 1: Smoking Levels by Ethnicity
Smoking Level African American Native Hawaiian Latino Japanese Americans White TOTALS
1-10 9886 2745 12831 8378 7650 41490
11-20 6514 3062 4932 10680 9877 35065
21-30 1671 1419 1406 4715 6062 15273
31+ 759 788 800 2305 3970 8622
TOTALS 18830 8014 19969 26078 27559 100450

## Analyze the Data

Suppose that one person from the study is randomly selected.

### Exercise 1

Find the probability that person smoked 11-20 cigarettes per day.

#### Solution

35,065100,45035,065100,450

### Exercise 2

Find the probability that person was Latino.

#### Solution

19,969100,45019,969100,450

## Discussion Questions

### Exercise 3

In words, explain what it means to pick one person from the study and that person is “Japanese American AND smokes 21-30 cigarettes per day.” Also, find the probability.

#### Solution

4,715100,4504,715100,450

### Exercise 4

In words, explain what it means to pick one person from the study and that person is “Japanese American OR smokes 21-30 cigarettes per day.” Also, find the probability.

#### Solution

36,636100,45036,636100,450

### Exercise 5

In words, explain what it means to pick one person from the study and that person is “Japanese American GIVEN that person smokes 21-30 cigarettes per day.” Also, find the probability.

#### Solution

471515,273471515,273

### Exercise 6

Prove that smoking level/day and ethnicity are dependent events.

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