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Lecture09-Blackboard - Lecture 9 Statistical Inference...

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Lecture 9 Statistical Inference: Hypothesis  Statistical Inference: Hypothesis  Testing for Single Populations Testing for Single Populations
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Learning Objectives Understand the logic of hypothesis testing, and know  how to establish null and alternate hypotheses Understand Type I and Type II errors, and know how  to solve for Type II errors Know how to implement the HTAB system to test  hypotheses Test hypotheses about a single population mean when  σ  is known Test hypotheses about a single population mean when  σ  is unknown
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Introduction to Statistical  Hypothesis Testing Hypothesis Testing A process of testing hypotheses about parameters by setting up null and  alternative hypotheses and using statistical techniques to reach  conclusions about the hypotheses Statistical Hypotheses a formal hypothesis structure consisting of the null hypothesis and the  alternative hypothesis, which together contain all possible outcomes of  the experiment or study Null Hypothesis The hypothesis that assumes the status quo – that the old theory,  method or standard is still true; the complement of the alternative  hypothesis  Alternative Hypothesis the hypothesis that complements the null hypothesis. Usually it is the  hypothesis that the researcher is interested in proving
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Null and Alternative  Hypotheses:  Example A manufacturer is filling 2 kg packages with flour They wish to determine if the packaging process  is out-of-control as determined by the weight of  the flour packages The null hypothesis indicates that there is no  problem with the packaging process, the  alternative hypothesis is that the process is out- of-control 0 a H : 2 kg H : 2 kg μ μ =
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Null and Alternative  Hypotheses:  Example A company has held 18% share of the market Because of an increased marketing effort they now  believe the company’s share is greater than 18% The null hypothesis indicates that the market share  is still 18% or has even dropped lower (converted to  a proportion), the alternative hypothesis is that the  market share is now greater than 18%. For  convenience, we can simply use = in the null  hypothesis 0 a H : 0.18 H : 0.18 p p =
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Null and Alternative  Hypotheses The Null and Alternative Hypotheses are  mutually exclusive.  Only one of them can be  true The Null and Alternative Hypotheses are  collectively exhaustive.  They are stated to  include all possibilities.  (An abbreviated form  of the null hypothesis is often used – see  previous slide) The Null Hypothesis is assumed to be true The burden of proof falls on the Alternative  Hypothesis
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