Stat1801 Probability and Statistics: Foundations of Actuarial Science Fall 2010-2011Chapter VIII Hypothesis Testing § 8.1 IntroductionHypothesis A statistical hypothesisis an assertion or statement about the population, usually formulated in terms of population parameters. It is denoted by or . 0H1HNull Hypothesis The null hypothesis, denoted by , is usually a statement about something that 0Hhas been established, or something that has an authoritative standing, or something worth protecting. Alternative Hypothesis The alternative hypothesis, denoted by , is usually a statement about something 1Hthat challenges the authority, or something that needs not be protected strongly. The hypotheses are often expressed in terms of the population parameters. However, there exists exceptional cases in non-parametricproblems. Example 8.1⎩⎨⎧≠=118:118:10μμHH, , ⎩⎨⎧≠=1:1:2120σσHH⎩⎨⎧≠=2112102:2:ppHppH⎩⎨⎧on.distributinormalnot isPopulation:on.distributinormalisPopulation:10HHDefinition A testof statistical hypothesis is a procedure, based upon the observed values of the random sample obtained, that leads to the rejection or non-rejection of the null hypothesis . 0HP.165
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