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# sec81 - Math 2311 Class Notes for Section 8.1 8.1 Inference...

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Math 2311 Class Notes for Section 8.1 8.1 - Inference for the Mean of a Population In chapter 7, we discussed one type of inference about a population – the confidence interval. In this chapter we will begin discussion the significance test . H 0 : is the null hypothesis. The null hypothesis states that there is no effect or change in the population. It is the statement being tested in a test of significance. H a : is the alternate hypothesis . The alternative hypothesis describes the effect we suspect is true, in other words, it is the alternative to the “no effect” of the null hypothesis. Since there are only two hypotheses, there are only two possible decisions: reject the null hypothesis in favor of the alternative or don’t reject the null hypothesis . We will never say that we accept the null hypothesis. For inference about a population mean: 0 0 : H μ μ = where 0 μ represents the given population mean. Alternate Hypothesis Rejection Region 0 : a H μ μ < 0 : a H μ μ > 0 : a H μ μ

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The probability, computed assuming that the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed is called the p -value of the test. A result with a small p -value is called
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