Marginal and Conditional Distributions
The contingency table below displays data from a survey on food preferences and exercise habits. A student assumes that the row totals represent the conditional distribution of exercise habits for a given food preference. What is the error in this assumption?
| 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 correctly deduced that the row totals indicate the conditional probabilities for exercise habits.
They confused the marginal distribution with a conditional distribution, erroneously assuming that row totals provide information about exercise habits conditioned on food preferences.
They mistakenly computed joint probabilities instead of marginal frequencies.
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