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Unformatted text preview: Lecture 9 Statistical Inference: Hypothesis Statistical Inference: Hypothesis Testing for Single Populations Testing for Single Populations 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 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 Null and Alternative Hypotheses: Example A manufacturer is filling 2 kg packages with flour They wish to determine if the packaging process is outofcontrol 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 ofcontrol a H : 2 kg H : 2 kg μ μ = ≠ 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 a H : 0.18 H : 0.18 p p = 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 Onetailed and...
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This note was uploaded on 08/22/2011 for the course FINC 2011 taught by Professor Craigmellare during the Three '10 term at University of Sydney.
 Three '10
 CraigMellare
 Corporate Finance

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