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A council plans a survey on a new bus route and wants a margin of error of at most 2 points with…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A council plans a survey on a new bus route and wants a margin of error of at most $2$ points with $95\%$ confidence. First it has no idea of the share. How many people must it ask? Then an earlier study suggests the share is near $0.1$ . How many people must it ask now?

Need a reminder? The key ideaShow

The interval for a proportion is $\hat p \pm 1.96\sqrt{\dfrac{\hat p(1 - \hat p)}{n}}$ . It needs a random sample with at least $10$ successes and $10$ failures. For a margin $m$ , $n \ge \left(\dfrac{1.96}{m}\right)^2 \hat p(1 - \hat p)$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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