lecture11-2 - Lecture 11 Chapter 13 The Chi Square Test of...

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Lecture’11 ’ Chapter 13 The Chi-Square Test of Independence A’hypothesis’test’is’a’procedure’that’tries’to’determine’whether’a’claim’about’a’ parameter,’ the’so -called’ null hypothesis ,’ has’enough’evidence’to’support’it.’The’ question’is’posed ’ in’the’negative:’Is’there’e nough’evidence’for’us’to’be’able’to’reject’ the’ null’hypothesis ?’ ’ Here’are’some’examples ’ of’claims’stated’as’null’hypotheses :’ ’ -’ 56%’of’voters’support’Candidate’A’(or’p=0.56) -the’mean’weight’of’American’men’is’179’pounds’(or’ μ =179)’ -’ two’categorical ’ variables’are’independent.’For’example,’stretching’before’ exercise’has’no’effect’on’the’chances’of’being’injured’during’exercise.’ The’chi -square’test’of’independence’covers’the’last’example.’It’tests’whether’a’ categorical’explanatory’variable’has’anythi ng’to’do’with’a’categorical’response’ variable.’The’null’hypothesis’says’ that’ it’doesn±t.’I f’this’is’true, ’ the’two’variables’are’ said’to’be’ independent .’In’the’ last’ example’above,’the ’ null’hypothesis ’ says’that’ stretching’prior’to’exercise’(explanatory’variable)’ does’ not’ increase’or’decrease’the’ rate’of’injury’during’exercise’(response’variable) .’The ’ alternative hypothesis ,’ says’ that’stretching’ does’ affect’the’rate’of’injury.’ In a chi-square test of independence, the null hypothesis always claims that there is no relationship between the explanatory and response variables.
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