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An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.

Modeling data distributions
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asked 2021-03-02

An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data.
\(\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 20 & 38 & 28 \\ \hline No\ hypertension & 50 & 27 & 18 \\ \hline \end{array}\)
Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.

Answers (1)

2021-03-03

Under the null hypothesis of the independence of hypertension and smoking status, we have the following expected table (rounding off the expected frequencies)
\(\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 33 & 31 & 22 \\ \hline No\ hypertension & 37 & 34 & 24 \\ \hline \end{array}\)
This gives the value of T to be 16.486, which, under the null, follows an asymptotic chi-squared distribution, with 2 degrees of freedom. This yields a p value of 0.00026, and hence we reject the null hypothesis.

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