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A made-up survey of 400 adults finds that a share of 0.62 recycle glass every week…

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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 made-up survey of $400$ adults finds that a share of $0.62$ recycle glass every week. Find the standard error. Find the margin of error at the $95\%$ level and at the $99\%$ level, to four decimal places. Find how many times wider the 99% interval is.

Need a reminder? The key ideaShow

In the long run, $95\%$ of the intervals made this way catch the true value. Multipliers: $1.645$ , $1.96$ and $2.576$ for $90\%$ , $95\%$ and $99\%$ . For a large sample, the interval for a mean is $\bar x \pm 1.96\dfrac{s}{\sqrt n}$ .

The worked solution

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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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