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Performing a Significance Test Regarding Population Mean

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Suppose that you perform a significance test regarding a population mean, and that the evidence does not warrant rejection of the null hypothesis. When formulating the conclusion to the test, why is the phrase "fail to reject the null hypothesis" more accurate than the phrase "accept the null hypothesis"? Please explain.

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This solution involves statistical testing.

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Suppose that you perform a significance test regarding a population mean, and that the evidence does not warrant rejection of the null hypothesis. When formulating the conclusion to the test, why is the phrase "fail to reject the null hypothesis" more accurate than the phrase "accept the null hypothesis"? Why can the null hypothesis not be proved? Please explain.

Answer:

If the null hypothesis is not rejected, the statistician does not then categorically conclude that the ...

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