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

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asked 2021-07-04

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.

Expert Answers (1)

2021-07-05

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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