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A made-up factory says that its bags of flour hold 500 g on average…

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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 factory says that its bags of flour hold $500$ g on average. An inspector weighs $49$ bags chosen at random and finds a mean of $502.4$ g with a sample standard deviation of $7$ g. Find the standard error of the mean. Find the 95% interval for the mean mass of all the bags, to two decimal places. Does the interval support the factory's claim of a mean of $500$ g?

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

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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