STAT 2 – SOME COMMENTS AND WARNINGS CONCERNING INFERENCE The confidence intervals and significance tests we have discussed concern the population mean μ and are based on the sample mean X . These mean-based inference procedures assume an SRS from a large population. Since the sample mean is not resistant to outliers, any outliers in the data have the potential to wreak havoc on these mean-based procedures. For example, they can affect the p-values of tests and the true confidence levels of confidence intervals. Our mean-based procedures assume that X is either normal or approximately normal. If the sample size n is large, this will be true by the central limit theorem. If n is small, then the population distribution must be normal or approximately normal for X to be normal or approximately normal. Even if one estimates the population mean μ accurately or finds a highly statistically significant result concerning the mean, keep in mind that the mean is only a summary of all the individuals in the population and doesn’t say anything about specific individuals
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