Ch 09 Hypothesis Testing.pdf - OPIM 550 MANAGERIAL...

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OPIM 550:MANAGERIAL STATISTICSFall 2018 EPChapter 9: Hypothesis Testing forSingle PopulationsRECALL: INFERENTIAL STATISTICS•Inferential Statistics is the process of usingsamples to make inferences about populations:•Two techniques:•Interval Estimates (Chapter 8)•Hypothesis Testing (Chapter 9)Sample StatisticPopulation ParameterMeanx̅μProportionp̂p2
WHAT IS HYPOTHESIS TESTING?
3EXAMPLE IN COMMON DAY EXPERIENCEEXAMPLE: (American Jurisprudence) A criminal trial isan example of hypothesis testing without the formalstatistics. In a trial a jury must decide between twohypotheses.•The null hypothesis isH0: The defendant is innocentThe alternative hypothesis or research hypothesisis Ha: The defendant is guilty
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HYPOTHESIS TESTING PROCESS5HYPOTHESIS TESTING TERMINOLOGY6
LET’S FORMALIZE THIS IN STATISTICS•To implement these ideas in a statistical frameworkwe need to define the following:•A hypothesis is a claim about a populationparameter(μ, p,σ2)•Possibly an assumption or longheld belief•Thenull hypothesis (H0)is thebenchmarkclaim to betested.•Is always about the population parameter, not about asample statistic.•Thealternative hypothesis (Ha)is the logical oppositeof the null hypothesis.7THE NULL VS. ALTERNATIVE HYPOTHESIS•Null hypothesis:•Begin with the assumption that the null hypothesis is true.•Similar to the legal notion of innocent until proven guilty•Refers to the status quo•May or may not be rejected – never accepted.•Alternative hypothesis:•Challenges the status quo•Is accepted if the null hypothesis is rejected•Often the hypothesis that the researcher wants todemonstrate!•The alternative hypothesis never contains the equality inany form. The relationship must be one of the following:<,, or >8
FORMAL “ACTUAL” STEPSStep 1: State the null and alternative hypothesesStep 2: Specify the level of significanceStep 3: Select the test statisticStep 4: Collect sample and testCritical Value*Determine critical value, rejection rule and computetest statisticOR pValue Approach* Compute test statistic and pvalueStep 5: ConcludeTwo common ways of doing this:Critical Value ApproachpValue approach9EXAMPLE 1• A company is interested in determining whether the correctamount of soft drink is being placed in 2liter bottles of sodaat the local bottling plant of a national softdrink company.

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