During the same week, a transit agency conducted two independent random surveys of adult residents of a city. Each survey was intended to estimate the proportion of all adult residents who had ridden a city bus during the previous month. The margins of error were determined using the same method.
| Survey | Estimated proportion | Margin of error |
|---|---|---|
| A | 43% | 5 percentage points |
| B | 47% | 3 percentage points |
Which choice identifies all conclusions that are supported by the survey results?
I. The proportion of all adult residents who rode a city bus during the previous month must be between 44% and 48%.
II. A proportion of 46% is plausible based on the results of both surveys.
III. The two survey estimates do not by themselves show incompatible results because their plausible ranges overlap.
IV. Survey B provides a more precise estimate than Survey A.