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Topic 17 Hypothesis Tests Text Reference Ravishankers...

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Topic 17. Hypothesis Tests Text Reference: Ravishanker’s Chapter 4 Reading Assignment: Ravishanker’s Sections 4.4 1/54
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In the ‘classical framework’, with point and interval estimation there was no supposition about the actual value of the parameter prior to collecting the data; using sampled data from the population, we are simply trying to determine the value of the population parameter. In hypothesis testing for population parameter(s), there is a preconceived idea about the value of the parameter, with two theories or hypotheses involved in the statistical study: I the established scientific view, or status quo (null hypothesis) I a challenge or alternative to the accepted view, suggesting change from the status quo (research or alternative hypothesis). 2/54
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Studies are generally conducted to challenge the null hypothesis. In statistical testing, we start by supposing the null hypothesis. I If the collected data does not support the null hypothesis, we reject the null hypothesis in favor of the alternative. I If it cannot be rejected we (tentatively) fail to reject the null hypothesis; we have not proven the null hypothesis, we have simply not been able to disprove the null hypothesis with these data. When deciding if the observed data support or do not support the null hypothesis, we must take variability of the sample into account. 3/54
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Example 17.1: Hazardous Waste Remediation (Statistical Test for Population Mean) DOE policy mandates remediation of a tank if the average radioactivity exceeds 100 rem. We, as DOE regulators, must decide if a given tank needs remediation; we will remediate only if there is sufficient evidence that it is needed. For example, does the mean tank radioactivity exceed 100 rem? The population of interest is all measurements taken from this specific tank, so we are interested in inference regarding population mean μ, i.e., I if μ 100 rem (null hypothesis), do not remediate I if μ > 100 rem (alternative hypothesis), remediate We don’t know μ, but the point estimator of μ from a sample is the sample mean, ¯ Y . To make inferences about μ based on ¯ Y , we must explicitly take the uncertainty in our estimator ¯ Y into account by using its sampling distribution. 4/54
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Elements of a Statistical Test (1) Null hypothesis H 0 . (2) Alternative (research) hypothesis H 1 (or H A ). (3) Test Statistic. (4) Rejection region (RR) or P-value. (5) Conclusion. Don’t forget to check any modeling assumptions you may have made! 5/54
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Two Hypotheses Hypotheses are statements about the population parameters . Let Θ denote the parameter space. Also let Θ 0 and Θ 1 denote a partition of Θ. i.e., Θ 0 Θ 1 = Θ and Θ 0 Θ 1 = . Null hypothesis : H 0 : θ Θ 0 The null hypothesis is the hypothesis that represents the accepted scientific view or that, most often, suggests no difference or effect.
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