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}}$
P10.5176442
P20.478428
P30.357624
P40.244121
P50.1648

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
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:

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Survey & $\boldsymbol{\sigma}$ & $\boldsymbol{N}$ & $\sqrt{\boldsymbol{N}}$ \\
\hline
P1 & 0.5 & 1764 & 42 \\
\hline
P2 & 0.4 & 784 & 28 \\
\hline
P3 & 0.3 & 576 & 24 \\
\hline
P4 & 0.2 & 441 & 21 \\
\hline
P5 & 0.1 & 64 & 8 \\
\hline
\end{tabular}
\end{center}

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