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

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

Question
Modeling data distributions
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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