Explain conditional probability and independence in everyday language and situations.
Assess whether association is established, mechanism-based, or data-dependent
Problem
With no data for \(\text{study}~\text{category}\) and \(\text{pass}/\text{fail}\), state whether association is determined, identify the conditional-rate comparison needed, and avoid a causal claim.
Big Picture
What this problem is really about
Variable names alone cannot establish association without comparable data. We’ll identify the missing within-category pass rates, define how each would be computed, set the comparison rule for similar versus meaningfully different rates, and withhold both association and causal claims until evidence is supplied.
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