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Chapter 8

Chapter 8

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University of Toronto St. George
Gillian Rowe

Chapter 8 Introduction to Hypothesis Testing 81 The Logic of Hypothesis TestingHypothesis testingstatistical method that uses sample data to evaluate a hypothesis about a populationone of the most commonly used inferential proceduresLogic underlying the hypothesistesting procedure 1 State a hypothesis about a population usually concerns the value of a population parameter 2 Use hypothesis to predict characteristics the sample should havesample should be similar to population but you should always expect a certain amount of error 3 Obtain a random sample from the population 4 Compare obtained sample data with the prediction made from the hypothesis If the sample mean is consistent with the prediction we conclude the hypothesis is reasonable If theres a big discrepancy between data and the prediction the hypothesis is believed to be wrongSituation where a researcher is using one sample to examine one unknown population y The Unknown Populationbegin with a known population set of individuals as they exist before treatment and goal is to determine what happens to the pop after the treatment is administered assume the population after treatment has the same shape as the original and the same standard deviation as the originaly Sample in the Research Studyactual research study is done with a sample not the population and the goal is to determine whether the treatment has any effect on the individuals in the populationnote the unknown population is hypothetical because treatment is never administered to the entire groupStep 1 State the HypothesesNull hypothesis Hin the general population there is no change no difference or no 0relationship In the context of an experiment Hpredicts that the independent variable 0 treatment has no effect on the dependent variable for the populationAlternative hypothesis Hthere is a change a difference or a relationship for the general 1population In the context of an experiment Hpredicts that the independent variable 1 treatment does have an effect on the dependent variable Step 2 Set the Criteria for a DecisionUse the data from the sample to evaluate the credibility of the null hypothesis Determine which sample means are consistent with the null hypothesis and which are not ex if the null states the pop mean should be 80 the sample mean should be around 80 The alpha levellevel of significancea probability value used to define the very unlikely sample outcomes if the null hypothesis is truethe alphavalue is a small probability that is used to identify the lowprobability samples ex with 005 we separate the most unlikely 5 of the sample means from the likely 95 of the sample means Critical regioncomposed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true The boundaries for the critical region are determined by the alpha level
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