1" Stat$401$–$Homework$3$$NOT$TURNED$IN$–$Complete$the$problems,$then$check$yourself$with$the$answers$that$are$posted$""1. The"authors"of"a"scientific"article"wrote"“Sixteen"rats"weighing"150"±"10"g"were"injected…”.""150"g"seems"to"be"the"average"weight"of"the"16"rats"in"the"sample.""The"10"g"figure"is"a"little"ambiguous"and"could"be"interpreted"in"several"different"ways.""(a) If"the"authors"wished"to"directly"convey"information"about"the"variation"among"the"weights"of"the"sixteen"rats"in"the"sample,"should"10"g"represent"the"sample"standard"deviation"or"the"standard"error"of"the"sample"average?""(b) Suppose"10"g"represented"the"standard"error"of"the"sample"average."What"was"the"sample"standard"deviation"of"the"16"rats?""(c) Suppose"150"±"10"g"represented"a"95%"confidence"interval"for"the"mean"weight"of"a"population"of"rats.""What"was"the"sample"standard"deviation"of"the"16"rats?""(d) Suppose"that"(b)"was"correct,"that"the"10"g"represented"the"standard"error"of"the"average"rat"weight.""Calculate"a"90%"confidence"interval"based"on"this"assumption.""""(e) Use"your"confidence"interval"in"(d)"to"make"a"conclusion"about"the"test"of"H0":""μ"="160"g"vs."Ha":""μ"≠"160"g."""2. A"cheese"company"suspects"that"a"milk"supplier"is"watering"down"milk"to"increase"profits.""The"freezing"point"of"natural"milk"follows"a"normal"distribution"with"mean"µ"="–0.545"degrees"Celsius"(C).""Added"water"raises"the"freezing"temperature"toward"0"degrees"C."The"freezing"temperature"of"15"randomly"selected"lots"of"the"supplier’s"milk"is"measured."The"average"of"the"15"measurements"is"!"="–0.538"degrees"C."The"standard"deviation"of"the"15"measurements"is"s"="0.008."Is"this"good"evidence"that"the"supplier"is"adding"water"to"the"milk?""(a) Write"down"the"null"and"alternative"hypotheses.""(b) Compute"a"test"statistic"(tZratio).""(c) Determine"the"pZvalue.""(d) Provide"a"scientific"conclusion."""" "2" 3.
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