1" Stat$401$–$Homework$4$Due$at$8$am$in$class,$Friday,$February$16$We$will$begin$enforcing$late$policy$–$papers$after$8$am$lose$20%$of$points$$$1. We"will"return"to"Homework"3,"problem"2"(not"turned"in"last"week),"and"extend"the"ideas.""""Suppose"6"pairs"of"hogs"are"used"in"an"experiment"to"determine"if"a"dietary"supplement"can"increase"weight"gain."Each"pair"of"hogs"are"full"siblings."One"sibling"is"randomly"assigned"to"receive"the"dietary"supplement."The"other"sibling"receives"a"supplement"that"does"not"contain"the"active"ingredient"believed"to"affect"weight"gain."The"gains"in"pounds"are"provided"below.""Sibling"Treatment"Weight"Gain"Placebo"Weight"Gain"1"70.4"69.3"2"38.2"37.2"3"59.7"58.7"4"40.3"39.3"5"93.5"92.5"6"50.7"49.6""Is"there"significant"evidence"that"the"supplement"increases"weight"gain?""""We’ll"look"at"two"different"ways"to"analyze"the"data.""Use"SAS""(PROC"TTEST)"to"perform"calculations"for"(a)"and"(b).""""In"reporting"your"answers"for"(a)"and"(b),"please"record"the"formula"you"would"use"to"calculate"the"test"statistic,"enter"the"values"into"the"different"parts"of"the"test"statistic,"and"then"the"value"of"the"test"statistic.""You"may"extract"the"values"to"plug"into"the"formulas"from"the"SAS"output.""As"before,"you"may"attach"your"program"and"output"if"you"would"like.""""(a) First"analyze"the"data"by"examining"the"mean"of"the"differences"in"weight"gain"for"each"sib"pair."Record"the"hypotheses,"test"statistic,"pYvalue,"and"state"a"conclusion."""(b) Now"analyze"the"data"by"assuming"that"the"two"columns"of"data"represent"independent"samples"from"two"populations"(hogs"treated"with"the"supplement"and"hogs"treated"with"the"placebo)."Record"the"hypothesis,"test"statistic,"pYvalue,"and"state"a"conclusion."""(c) Which"analysis"of"the"data"is"correct?"Briefly"explain"why.""""(d) Explain"what"features"of"the"data"cause"the"results"of"the"two"analyses"to"differ."""""2" "2. Read"exercise"12"on"p."51"in"Chapter"2.""Use"the"study"information"in"the"problem"description"to"complete"the"following.""(a) Calculate"a"95%"confidence"interval"for"the"difference"between"the"mean"birth"weight"for"mothers"who"used"marijuana"during"pregnancy"and"the"mean"birth"weight"for"mothers"who"did"not"use"marijuana"during"pregnancy.""(b) We"are"going"to"use"the"confidence"interval"to"make"tYtest"inferences.""What"are"the"null"and"alternative"hypotheses"for"the"inference"using"the"interval"in"(a)?""""(c) What"do"you"know"about"the"pYvalue"from"(a)?""""(d) Write"a"conclusion"for"the"question"of"whether"there"is"a"difference"based"on"the"information"you"have"about"the"pYvalue"in"(a)"Y"(c).""(e) Now"conduct"a"tYtest"that"explores"the"same"question"as"your"confidence"interval.""Be"sure"to"record"the"null"and"alternative"hypotheses,"the"tYstatistic,"pYvalue"and"a"scientific"conclusion.""(f) Are"the"conclusions"in"(d)"and"(e)"consistent"or"contradictory?"""""3.
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