# Problem 1A Determination of Confounding Factors usinga Test of IndependenceAge and Obesity FrequenciesObeseNot obeseTotalAge500100600

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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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