# Method of calculating sample variance denominator

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Methodofcalculatingsamplevariancedenominatornumerators2Sourceofvariationd.f.sumofs uaresmean s uares~/w~f3-1~Lf1.'-t39.f-2_XIfthe alternative hypothesis is true, that will tend to make the "Between sample" variance largerthan the "Within sample" variance.But we also realize that could happenjustby chanceofsampling,ifthe null hypothesis were true.How dowedecide which has more likely happened here?The F-statisticiscalculatedasthe ratiooftwo variances:F-observed=BetweensamplevarianceWithinsamplevariance11
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Chapter 14 / Exercise 56
Nature of Mathematics
Smith
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Oops!! !I left out an important aspectofhow this experiment was conductedAfterthesampleof15pastordershadbeenselected,5differentjobberswererecruitedtohelpwiththeexperiment.Threeorderswererandomlyassignedtoeachjobber,andeachjobberrandomlyassignedhis/herorderstothethreedifferentprocedures.So the layoutofthe study really looked like:Procedure123HarryEthelArthurRandyTomThe numerical summary results were correctasoriginally provided How will this newinformation affect the ANOVA table?Sourceofvariationd.f.sumofsquaresmean squares~s~{~L.'l,C(.5:>~Z.-~~1~(l5-(.-:,l1&(~-tf'33Xf)12
Wecan reject the null hypothesis,andwe conclude that not all the gasoline types have the samepopulation mean.Buthow different is AfromB? AfromC?BfromC?Weknow how to build a confidence intervalforthe difference between population means:Supposewedid construct those different confidence intervals, each with 95% confidence. Howconfident couldwebe thatALL3ofthe intervals provide correct claims?A methodology for constructing all the possible confidence intervalsfor difference between2population means, with an associated "familyconfidence coefficient" that all the constructed intervals are correctstatements.

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Term
Spring
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Ahrens,MarkE
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Chapter 14 / Exercise 56
Nature of Mathematics
Smith
Expert Verified