An electoral research institute receives an order in which the margin of error should be at most 2 percentage points (0.02).
The institute has 5 recent surveys, P1 to P5, on the subject of the order and will use the one with an error smaller than requested.
The data on the surveys are as follows:
| Survey | $\boldsymbol{\sigma}$ | $\boldsymbol{N}$ | $\sqrt{\boldsymbol{N}}$ |
| P1 | 0.5 | 1764 | 42 |
| P2 | 0.4 | 784 | 28 |
| P3 | 0.3 | 576 | 24 |
| P4 | 0.2 | 441 | 21 |
| P5 | 0.1 | 64 | 8 |
The error $e$ can be expressed by
$$|e| < 1.96 \frac{\sigma}{\sqrt{N}}$$
where $\sigma$ is a parameter and $N$ is the number of people interviewed by the survey. Which survey should be used?
(A) P1
(B) P2
(C) P3
(D) P4
(E) P5