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In a made-up town, 60% of the adults support a new market…

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

In a made-up town, 60% of the adults support a new market. A survey goes to a random sample of adults. Supporters reply 50% of the time and the others 20% of the time. Out of every 100 adults asked, how many replies come back? What percentage of the replies support the market? Give the second answer to one decimal place.

Need a reminder? The key ideaShow

When two groups reply at different rates $r_y$ and $r_n$ , the share of the first group among the replies is $\dfrac{p\,r_y}{p\,r_y + (100 - p)\,r_n} \times 100\%$ . A larger sample shrinks the luck, about $\pm 2\sqrt{\dfrac{q(100 - q)}{n}}$ percentage points, but never the bias.

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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