APFIVE In a survey examining food preferences and exercise habits, a researcher constructs a contingency table. The student then assumes that the row totals (marginal frequencies) represent the conditional distribution of exercise habits given a food preference. What is the mistake in this analysis?
| Food Preference | Exercises Regularly | Does Not Exercise | Total |
|---|---|---|---|
| Healthy | 30 | 20 | 50 |
| Unhealthy | 10 | 40 | 50 |
| Total | 40 | 60 | 100 |
They applied a chi-square test without verifying that the sample size requirements were met.
They confused the marginal distribution with a conditional distribution, erroneously assuming that row totals provide information about exercise habits conditioned on food preferences.
They correctly deduced that the row totals indicate the conditional probabilities for exercise habits.
They mistakenly computed joint probabilities instead of marginal frequencies.
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