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## Chapter 12. Constructing Confidence Intervals: Guessing with Confidence

Sometimes samples don’t give quite the right result.

You’ve seen how you can use point estimators to estimate the precise value of the population mean, variance, or proportion, but the trouble is, how can you be certain that your estimate is completely accurate? After all, your assumptions about the population rely on just one sample, and what if your sample’s off? In this chapter, you’ll see another way of estimating population statistics, one that allows for uncertainty. Pick up your probability tables, and we’ll show you the ins and outs of confidence intervals.

## Mighty Gumball is in trouble

The Mighty Gumball CEO has gone ahead with a range of television advertisements, and he’s proudly announced exactly how long the flavor of the super-long-lasting gumballs lasts for, right down to the last second.

Unfortunately...

Mighty Gumball used a sample of 100 gumballs to come up with a point estimator of 62.7 minutes for the mean flavor duration, and 25 minutes for the population variance. The CEO announced on primetime television that gumball flavor lasts for an average of 62.7 minutes. It’s the best estimate for flavor duration that could possibly have been made based on the evidence, but what if it gave a slightly wrong ...

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