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A coin is fair, so the true share of heads is 0.5…

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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 coin is fair, so the true share of heads is $0.5$ . Find the standard error of the share of heads in $100$ tosses. Find it for $400$ tosses.

Need a reminder? The key ideaShow

Here is the standard error of a sample share.

\displaystyle SE = \sqrt{\dfrac{p(1 - p)}{n}}.

Four times the sample halves it. The population size hardly matters unless the sample is a large part of it.

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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