CONTINGENCY TABLES AND THE CHI-SQUARE TESTObservedExpectedCONTINGENCY TABLES AND THE CHI-SQUARE TEST2-way tables: describe data in multiple categoriesSimpson’s Paradox 3-way tables(3 variables)Total Engineering EnglishMale Female Male Female Male FemaleAdmit 35 20 55 30 10 5 10Deny 45 40 85 30 10 15 3080 60 140 60 20 20 40Row variable / column variableIs there enough evidence to support discrimination?Department is a hidden variable that completely reversed the association of gender and acceptance. English is hard to get into and more females applied.Hypothesis Testing - when expected counts are large enough (p. 545)Treating Cocaine AddictionCompare an antidepressant called Disipramine with a std trt (Lithium)Is there a statistically significant difference? Observed Success FailureDesipramine 14 10 24Lithium 6 18 24Placebo 4 20 2424 48 72Ho: no difference Vs. H1: there is a differenceExpected Count (page 533) =(row total * column total)/table totalExpected Success FailureDesipramine 8 16 24Lithium 8 16 24Placebo 8 16 2424 48 72Chi Square statistic(page 536) = 4.5 + .5 + 2 + 2.25 + .25 + 1 = 10.5Reject Ho if X2 > X2 (r-1)(c-1)() = X2 2 (.05) = 5.99p-value between .01 and .005 (99-99.5% confident there is a difference)Page 1 of 2Xobs22( exp)exp( ) ( ) ( ) ( ) ( ) ( )14 886 884 8810 161618 161620 16162 2 2 2 2 21) How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers assigned newly laid eggs to 1 of 3 temperatures: hot, neutral, cold. Hot duplicates the extra warmth provided by the mother python and cold duplicates the absence of the mother. Observed NotHatchedHatched Total Expected NotHatchedHatched TotalCold 11 16 27 ColdNeutral 18 38 56 NeutralHot 29 75 104 HotTotal TotalResearchers believe eggs will be less likely to hatch in cold water. Does Temperature have a significant effect on hatching?State the null and alternative Hypothesis.Give the test statistic X2Give the p-valueDo you reject or fail to reject Ho? Does Temperature have a significant effect on hatching2) Majors for men and women in business. We sent questionnaires to 722 members of the senior class in the college of Business Administration at the University of Illinois. One question asked which major within the business program the student had chosen.Obs Accounting Administration Economics Finance ExpFemale 69 91 5 61Male 56 40 6 592_a) 2 of the observed cell counts are small, are the expected cell counts large enough to use the chi-square approximation? (p. 628)2_b) Is there a statistically significant relationship between gender and major of business students?State the null and alternative Hypothesis.Give the test statistic X2Give the p-valueDo you reject or fail to reject Ho? Does gender significantly impact the major of business students?2_c) What % of the students did not respond to the questionnaire? Does this weaken our results?Page 2 of