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Please explain this concept?

If the claim says that the population mean is greater than 200 and the sample mean is 215, we can say that the claim is true even without a formal test.

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  • 1 decade ago
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    No. The population mean could be 200 or less, but our sample just contains unusually high values in the population. Say there are just six cases in the population with values of 110, 140, 170, 200, 230 and 260. The population mean is 185. But if the sample consists of two cases and they happen to have values of 200 and 230, then the sample mean is 215.

    A sample can only ever give an estimate of the population statistics. A formal test will give us an indication of how accurate that is likely to be, given the numbers of cases in the sample and in the population.

    The bigger the sample the more accurate the estimate. But even with a sample of four cases in the example above, the sample mean could still be 215. In reality, you would only know about the cases in the sample, so in this example, there would be no indication available as to whether the population mean was less than 200 or more than 230. But a statistical test would allow you to calculate the probability that the population mean is within that range. You could then say with a specific amount of confidence (eg 80%) that the population mean is more than a given amount (eg 200).

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