Problem

Use the \(\text{two}\text{-}\text{way}~\text{table}~\text{information}\) to evaluate whether there is an association: \(P(\text{bus}|\text{freshman})=0.40\) and \(P(\text{bus}|\text{sophomore})=0.42\).

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What this problem is really about

Association is judged by comparing the same outcome’s conditional rate across groups and considering the size of the gap. We’ll align the two bus-use rates, subtract to find their percentage-point difference, assess practical similarity, and avoid labeling every nonzero difference as strong evidence.

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There is an association because 0.40 and 0.42 are different.

No association is shown because both probabilities are less than 0.50.

There is a strong association because sophomores are much more likely to take the bus.

Little or no association; the conditional rates are about the same.

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Use the \(\text{two}\text{-}\text{way}~\text{table}~\text{information}\) to evaluate whether there is an association: \(P(\text{bus}|\text{freshman})=0.40\) and \(P(\text{bus}|\text{sophomore})=0.42\).

What this problem is really about

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