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Statistical analysis typically involves reaching a decision or making an inference in spite of the variation in data. In most problems, this variation conceals important characteristics of the population. The more variation in the data, the harder it becomes to make precise statements about the population. On the other hand, as the sample variance s2 gets smaller and smaller, the 95% confidence intervals for μ close in tighter and tighter and we learn where μ is. As s2 approaches 0, the confidence interval collapses to a single point.
There are important cases, however, when s2 = 0, but nonetheless we don’t know the population parameter. The following three examples illustrate such cases.
Clinical Trials
The Food and Drug Administration ...
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