Question
Asked Nov 10, 2019
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Problem 1A Determination of Confounding Factors using
a Test of Independence
Age and Obesity Frequencies
Obese
Not obese
Total
Age
500
100
600
<50
50+
200
200
400
Total
1000
300
700
A. Are age and obesity independent? Perform a y2 test of independence.
Remember to document the five steps used in hypothesis testing.
JONES& BARTLETT LEARNING
Chart Your Own Course
O2011 Jones & Bartlett Learning, LLC
www.jblearning.com
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Problem 1A Determination of Confounding Factors using a Test of Independence Age and Obesity Frequencies Obese Not obese Total Age 500 100 600 <50 50+ 200 200 400 Total 1000 300 700 A. Are age and obesity independent? Perform a y2 test of independence. Remember to document the five steps used in hypothesis testing. JONES& BARTLETT LEARNING Chart Your Own Course O2011 Jones & Bartlett Learning, LLC www.jblearning.com

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Expert Answer

Step 1

Let us first test whether the “age” and “obesity” are independent or not, using a Chi-square test of Independence. If the two variables are found not to be independent, then, by observing the change in the proportions, it can be decided whether the age of an individual is independent of obesity.

Step 2

Hypotheses:

The null hypothesis is:

H : The age and obesity are not attribute differently.

The alternative hypothesis is:

H : The age and obesity are attribute differently.

Step 3

Calculation steps:

The calculations have been done in EXCEL.

Denote oij as the observed frequency for ith row and jth column (i =1, 2; j =1, 2) and eij as the expected frequency for ith row and jth column.

Table 1 provides the data values, oij.

Table 2 calculates the row proportions: (cell value)/(row total) = oij / oi∙ so that, the first row proportion will be 100/600 ≈ 0.1667. Similarly, the others can be calculated.

Table 3 calculates the expected frequencies under the independence assumption. If independent, ...

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Statistics

Hypothesis Testing

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