Question

In an air pollution study, a random sample of 200 households was selected from each of 2 communities. A respondent in each house was asked whether or not anyone in the house was bothered by air pollution. The responses are tabulated below:
Community Yes No Total
I 43 157 200
II 81 119 200
Total 124 276 400
Can the researchers conclude that the 2 communities are bothered differently by
air pollution? (a = 0.05)

Answer 1

Answer on Question #46504 – Math – Statistics and Probability

In an air pollution study, a random sample of 200 households was selected from each of 2 communities. A respondent in each house was asked whether or not anyone in the house was bothered by air pollution. The responses are tabulated below:

Can the researchers conclude that the 2 communities are bothered differently by air pollution? ($\alpha = 0.05$)

Solution

$H_0$: the two populations are bothered similarly by air pollution.

$H_1$: the two populations are bothered differently by air pollution.

$$\chi^2 = \frac{400(|43 \cdot 119 - 81 \cdot 157| - 0.5 \cdot 400)^2}{124 \cdot 276 \cdot 200 \cdot 200} = 16.$$

From percentiles of the chi-square distribution table,

$$\chi_{(1-\alpha),df}^2 = \chi_{(0.95),1}^2 = 3.841.$$

Statistical decision: reject $H_0$, since $\chi^2 > 3.841$.

Clinical decision: Conclude that, on the basis of these data, the 2 communities are bothered differently by air pollution.

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