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where X is the sample mean, ^ is the known mean of the population, ct is the population standard deviation, and n is sample size. This test statistic is the difference between the sample and overall mean, X - divided by the standard deviation of the sample mean, ct/Hw. It describes the difference between the sample and population means in "standardized units." A confidence interval for the true mean ^ is from X - z(a-/Mn) to X + z(a7-Hn), where z is the value from the normal table in Appendix C corresponding to the relevant confidence level.

As seen in Figure 3.2, 95 percent of the area under the z statistic's normal or bell-shaped curve falls within ± 1.96 standard deviations of the mean; 99 percent of this area falls within ± 2.576 standard deviations. In other words, there can be 95 percent confidence that the sample is typical of the overall population if the sample average falls within roughly two sample stan-

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