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23Homing in on the Population Mean II

Let's look at this from the perspective of one of the surveyors (you).

As the lone surveyor, you will want to construct a 95% confidence interval around your sample mean of 4.15 to check whether it contains 4.0. Since the true population variance in this scenario is unknown—as is usually the case in practice—the sample variance is used instead.

Note: Using the sample variance as an estimate of the population variance introduces additional uncertainty. We won't address this source of uncertainty until Chapter 27.

Let's simulate the uncertainty surrounding our sample mean of 4.15. We'll simulate 1000 random samples of size 100 based on the scenario's mean of 4.15 and variance of 1.0. Given the results shown in Figure 23.1, it appears that 4.0 is not especially unlikely. Eyeballing, the 95% confidence interval appears to be about 3.95–4.35. Given this, we would not rule out the hypothesis that the true population mean could be 4.0. ...

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