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PSYB07H3 (20)


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Douglas Bors

AFTER MIDTERM EXAM NOTESTTESTONESAMPLE TTEST2 22ifis known and is unknown we must estimatewith s ie if you dont know the population variance use the sample variance to estimatebecause we use s we can no longer declare the answer to be a z but rather it is a tWHY 2the sample variance s is an unbiased estimator of the population 222variancebut s is not a normal distributions tends to be positively skewed if z is used we more often underestimate 2population variancethan overestimate esp with a small n underestimating is more of a bigger mistake THEREFORE the z table cannot be used as the t is likely to be larger 2than z because s is in the denominatorz table can be only used in this situation if we have an infinity observations but this is nevert table has critical values instead of tvalues Differences in formulas22vs substitute s for xxxmmmxxxmmmzt22sSsSsSxxNNNN To treat t as a Z would give us too many significant resultsTherefore for the students t distribution we switch to the ttable 2when we use sunlike the z the distribution is a function of the degrees of freedom with ninfinity and tzz196 but for t value is dependent of degrees of freedomwith an infinity number of df it approaches 196for onesample cases degrees of freedom dfn1for samplebut if givenno need for n1 just n21 df is lost because we usedsample mean to calculate sx0 all x can vary save for 1Example 1 the effect of statistic tutorialsLast 100 years 760 no tutorialsThis years 793 tutorialsN20s641 State the null and the alternative hypothesisH 76H 7601
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