Toreceivefullcredit,you must

• Showallthe relevant stepsused to arrive atyour solutions.
• Clearly state any necessaryassumptions and/orconclusionsmade.
• Write ina clear, concisemanner and donot include raw statisticaloutputorcode unless it isabsolutely necessary. Theresultsofyour analysis should be edited forrelevance.
• Figures and tablesmustbelabeledandcaptionedor described inthe textoftheassociated answer.

1. Bloodpressure -11 points:

Datacollectedthrough theNationalHealthandNutritionExaminationSurveyindicatethatthat,intheUnitedStates,systolicbloodpressureforindividuals18andolderisapproximatelynormallydistributedwith=123 mm Hg andSEM=0.3.

1. Inthisproblem, standarderrorofthemeanisgiven ratherthanstandarddeviation.Describethedifferencebetweenthetwo,bothfromamathematical/equationstand pointandapractical/functionalstandpoint. (3pts)
2. Ifthe sizeof this sampleis n=19,930, what is the sample standard deviation? (2 pts)
3. Whatpercent ofsamplesofanequalsizewouldyouexpect tohaveameansystolic bloodpressuregreater than 122.25 mgHg?(3 pts)
4. Approximatelywhatpercent ofindividuals18andolderintheUnitedStates wouldyouexpecttohavehigh blood pressure(asystolic blood pressurereading greaterthan 140 mm Hg)?(3 pts)

1. Framinghamstudy (fromPrinciples of Biostatistics, Pagano, Gauvreau)-13 points:

IntheFraminghamstudy,serumcholesterollevelsweremeasuredforalargenumberofhealthymales.Thepopulationwasthenfollowed for16years.Attheendofthistime,themenweredivided intotwogroups:thosewhohaddevelopedcoronaryheartdiseaseandthosewhohadnot.Thedistributionsoftheinitial serum cholesterol levels for each group were found to be approximately normal. Among individuals

whoeventuallydevelopedcoronaryheartdisease, themeanserumcholesterollevelwas=244mg/100mlandthestandarddeviationwasSD=51mg/100ml;forthosewhodidnotdevelopthedisease,themeanserum cholesterol levelwas=219 mg/100 ml and the standard deviation was SD=41 mg/100 ml.

1. Supposethataninitial serumcholesterollevelof260mg/100mlorhigherisusedtopredictcoronaryheartdisease.Whatistheprobabilityofcorrectly predictingheartdiseasefor amanwhowilldevelopit?(3 pts)

Asahintforpartsb-dbelow,thinkaboutwhatpartofthegraphs(i.e.whatportionoftheareaundereachofthenormalcurvesdescribedintheproblem)representsdeveloping/notdevelopingheartdisease andalsowhatpartofthesegraphsrepresents failingtopredictheartdisease, ifaninitial serumcholesterollevelof260 mg/100 ml or higher is used to predict coronary heart disease.

1. What is the probability of failing to predict heart diseasefor a manwho will not develop it?(3 pts)
2. What is the probability of failing to predict heartdisease for aman who will develop it?(3 pts)
3. Whatwouldhappen totheprobabilitiesoffalsepositive andfalsenegative errorsifthe cutoffpointforpredicting heart diseaseis lowered to 250 mg/100 ml?Why?(3 pts)
4. In this population, does initial serum cholesterol level appear to beuseful for predicting coronary heartdisease?Why or why not? (1 pt)