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10-09 math - Notation Notation and Equations for...

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Notation’and’Equations’for’ Single-Sample’ t-test’Lecture ’ 10/9’ Notation’ μ 0 :’The’value’of’the’population’mean’assumed’by’the’null’hypothesis ’ in’a’basic’t -test’ t :’t’statistic’ –’ an’inferential’statistic’measuring’the’reliability’of ’ the’difference’ between’ M ’ and’ μ 0 df :’degrees’of’freedom;’determines’which’t’distribution’to’use Formula’for’t’statistic ’ (single-sample’ t-test).’The’t’statistic’tells’how’reliable’the’ difference’is’between’a’sample’mean’( M )’and’a’hypothesized’population’mean’(µ 0 ).’ It±s’our’first’ example’of’a’purely’inferential’statistic,’ because’ its’value’doesn±t’have’ any’physical’meaning.’If’ t ’ =’3,’this’do esn±t’mean’three ’ of ’ anything;’it’just’means’we’ can’be’fairly’confident’that’µ 0 ’ is’not’the’true’population’mean.
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