1" Stat$401$–$Homework$5$Due$at$8$am$in$class,$Friday,$February$22$We$will$be$enforcing$late$policy$–$papers$after$8$am$lose$20%$of$points$$$1. Read"exercise"18"on"p."76"in"Chapter"3.""A"starter"SAS"program"is"posted"called"metabexpend.sas."(a) Can"cause"and"effect"be"inferred"from"this"study?""Explain"why"or"why"not."(b) Can"this"study"be"generalized"to"all"patients"served"by"this"hospital?""Explain"why"or"why"not."(c) Conduct"a"tGtest"to"evaluate"whether"mean"metabolic"expenditure"varies"in"relation"to"whether"a"patient"was"admitted"for"multiple"fractures"(a"form"of"trauma).""Be"sure"to"record"the"null"and"alternative"hypotheses,"the"tGstatistic,"pGvalue"and"a"scientific"conclusion"that"is"consistent"with"the"design"of"the"study."""(d) Use"SAS"to"evaluate"the"assumptions"of"the.""Two"of"the"assumptions"for"the"2Gsample"tGtest"are"homogeneous"variances"and"normality"of"observations.""Comment"on"whether"each"of"these"assumptions"is"being"met"and"whether"you"think"the"tGtest"is"robust"in"this"situation."(e) Is"the"difference"between"the"sample"averages"for"each"group"resistant?""Explain."(f) The"book"lists"the"ranks"of"the"data."The"ranks"are"calculated"by"combining"the"metabolic"expenditure"data"(Y)"from"both"groups,"and"then"sorting"these"values"from"smallest"to"largest.""When"you"do"this,"you"want"to"keep"the"group"membership"with"the"sorted"value"of"Y"so"you"can"tell"which"group"it"belongs"to.""The"rank"of"1"is"assigned"to"the"smallest"observation"(18.8),"a"rank"of"2"to"the"second"smallest"observation"(20.0),"and"so"on"up"to"the"largest"value"(38.5),"which"has"the"rank"of"15"(="n).""When"two"values"are"the"same"(there"are"two"values"of"20.9,"for"example),"the"two"(or"more)"ranks"that"correspond"to"those"values"are"averaged"and"the"average"rank"is"assigned"to"all"observations"with"the"common"value"(for"the"two"20.9s,"the"ranks"of"4"and"5"are"averaged"to"get"4.5)."""Verify"the"ranking"of"the"data"as"expressed"in"the"second"table"of"this"problem"by"making"a"list"of"the"sorted"observations,"each"observation’s"group"membership,"and"the"rank"of"each"observation."(g) Calculate"the"average"rank"for"each"group.""Is"the"difference"between"the"average"ranks"for"the"two"groups"resistant?""Explain.""" "2" "2. A"researcher"wanted"to"compare"the"abundance"of"crabs"in"two"different"coastal"areas.""Each"coastal"area"was"divided"into"several"hundred"strips.""Each"strip"had"approximate"dimensions"of"10"feet"by"300"feet"and"was"oriented"roughly"perpendicular"to"the"shoreline.""A"random"sample"of"20"strips"was"selected"from"each"of"the"coastal"areas.""With"the"help"of"a"Global"Position"System"(GPS)"device,"the"researcher"walked"each"of"the"randomly"selected"strips"and"recorded"the"number"of"crabs"observed"in"each"strip.""The"natural"log"of"the"count"in"each"strip"was"computed.""Summary"statistics"for"the"coastal"areas"are"provided"below.""Coastal"Area"Number"of"Strips"Average"of"Log"Counts"Standard"Deviation"of"Log"Counts"A"20"1.88"1.1"B"20"2.75"1.2""(a) Is"the"investigation"described"in"this"problem"an"observational"study"or"a"randomized"experiment?""What"kind"of"statistical"inferences"can"you"make"with"this"design?"(b) Estimate"the"difference"between"the"mean"log"crab"count"per"strip"in"coastal"area"B"and"the"mean"log"crab"count"per"strip"in"coastal"area"A."(c) BackGtransform"the"estimated"difference"between"the"mean"log"crab"count"per"strip"in"coastal"area"B"and"the"mean"log"crab"count"per"strip"in"coastal"area"A."""(d) What"population"quantity"(in"original"scale)"is"being"estimated"in"(c)?"(e) Find"a"95%"confidence"interval"for"the"difference"in"mean"log"crab"counts"between"the"two"coastal"areas."(f) Find"a"95%"confidence"interval"in"the"original"scale"for"the"population"quantity"in"(d)."(g) Using"the"work"your"answers"from"(a)G(f),"provide"a"summary"of"your"findings"for"comparing"the"abundance"of"crabs"in"the"two"coastal"areas.""Be"sure"to"include"an"evidence"statement,"an"estimate"and"a"measure"of"precision"for"the"estimate.""(Do"not"calculate"a"test.)""" "3" "3. A"researcher"conducted"a"study"to"determine"if"the"lead"question"could"influence"students'"guesses"about"the"population"of"California."Such"an"influence"would"support"a"phenomenon"in"psychology"known"as"anchoring.""Anchoring"is"often"used"by"advertisers"or"salespeople"to"try"to"get"customers"to"pay"a"high"price"for"an"item"while"believing"that"it"is"a"bargain"compared"to"some"other"option."The"researcher"recruited"38"students"for"the"study.""Of"these"students,"21"were"randomly"assigned"to"be"asked"if"the"population"of"California"was"greater"or"less"than"7"million"–"this"is"the"“7”"million"treatment"group.""The"remaining"17"students"were"asked"if"the"population"of"California"was"greater"or"less"than"70"million"–"this"is"the"“70”"million"treatment"group."""The"next"question"was"given"to"all"students"(in"both"“7”"and"“70”"million"treatment"groups),"who"were"asked"to"guess"the"population"of"California"in"millions.""The"program"california.sas"on"the"course"web"site"contains"data"from"this"study"and"code"for"creating"a"variable"called"Z,"which"logGtransforms"Y"for"analyses"in"part"(f)G(h).""""(a) Is"the"investigation"described"in"this"problem"an"observational"study"or"a"randomized"experiment?""What"kind"of"statistical"inferences"can"you"make"with"this"design?"(b) Use"what"we"learned"in"Lab"5"to"evaluate"whether"the"assumptions"of"the"tGtest"hold"for"the"original"scale"data."""(c) Regardless"of"(b),"use"SAS"to"conduct"a"twoGsample"tGtest"in"the"original"scale.""For"your"answer,"report"a"null"and"alternative"hypothesis,"test"statistic,"pGvalue,"and"a"conclusion"for"testing"whether"the"first"question"had"an"effect"on"the"students'"guesses."(d) Provide"a"95%"confidence"interval"for"the"difference"between"the"mean"guess"of"the"“7”"million"group"and"the"mean"guess"of"the"“70”"million"group."(e) As"in"(b),"evaluate"whether"the"normality"and"homogeneous"variance"assumptions"of"the"tGtest"hold"for"the"(natural)"logGtransformed"data."""(f) Regardless"of"(e),"use"SAS"to"perform"the"2Gsample"tGtest"on"logGtransformed"data."Report"relevant"null"and"alternative"hypotheses,"test"statistic,"pGvalue,"and"conclusion."(g) Provide"a"95%"confidence"interval"for"the"difference"between"the"mean"log"CA"population"guess"of"the"“7”"million"group"and"the"mean"log"CA"population"guess"of"the"“70”"million"group."(h)
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