Problem — Sample size for a 1 percent error

Text

How many respondents are needed for an electoral poll with a margin of error $\le 1\%$ at the $95\%$ confidence level?

Solution

Set-up. For a proportion the margin of error is $E = z\sqrt{\frac{p(1-p)}{n}},$ with $z\approx 1,96$. In the worst case $p=0,5$, so $p(1-p)=0,25$. Imposing $E \le 0,01$ and solving for $n$: $n \ge \frac{z^2\,p(1-p)}{E^2} = \frac{1,96^2\cdot 0,25}{0,01^2}.$ Compute this value (of the order of a few thousand) and round up to the next integer: that is the minimum number of respondents.

Links

Topics: Probabilita
Concepts: Intervallo di confidenza · Margine di errore
Skills: Stimare
Exercise type: Problema modellizzazione