1. 1
PRBE002 – DecisionMaking
AssessmentItem3:
Your PRBE002 unitInformationdescribedthe focusof assignmentasfollows:
Description/Focus: AssessmentItem3– ProblemSolvingTask2 – Solvingasetof givenproblems
throughthe applicationof statistical andotherdecisionmakingtechniques
Value: 50%
Length: n/a
Task: As detailedinthe assignmentinstructions.Please AnswerALL the questions
clearly.Please show all yourcalculations.
Preparation: Studentsare to applythe statistical conceptsandtechniquesintroducedin
Weeks7-11 topractical businessdecisionmakingproblems.
Presentation: Assignmentsmustbe typedfordescriptiveandanalytical segmentsof your
assignmentsandall yourcalculationsneatlyhandwrittenandsubmittedvia
Learnline. Explainyouranswerfully.Show all yourworkingsclearly.
Assessmentcriteria: Clearindicationsof anyassumptionsmade and logical settingoutof applications
of appropriate statisticaltechniques,plusthe abilitytomake informeddecisions
basedon evidenceprovidedbyuse of these techniques.
Illegible answerswill notbe markedandwill automaticallyreceiveagrade of
zero.
AnswerAll Questions
Question1:
Many people sleeplate onthe weekendstomake upfor“short nights” duringthe workweek.
The BetterSleepcouncil reportsthat61% of us getmore than 7 hoursof sleeppernightonthe
weekend.A randomsample of 350 adultsfoundthat235 had more than 7 hours of sleepeach
nightlastweekend.Atthe 0.05 level of significance,doesthisevidence show thatmore than
61% sleep7hours or more pernighton the weekend?
(https://books.google.co.id/books?id=DWCAh7jWO98C&pg=PA503&lpg=PA503&dq=,+does+thi
s+evidence+show+that+more+than+61%25+sleep+7+hours+or+more+per+night+on+the+weeke
nd&source=bl&ots=myKrmPIkVQ&sig=7aJkS9VSGr-
WxsktJRdmnDD8Eyc&hl=en&sa=X&ei=om5YVdvHDoy8ugTZ9IGwCw&redir_esc=y#v=onepage&q
=%2C%20does%20this%20evidence%20show%20that%20more%20than%2061%25%20sleep%2
07%20hours%20or%20more%20per%20night%20on%20the%20weekend&f=false)
2. 2
(5 marks)
Question2:
For years,manylarge companiesinMelbourne have usedareputable employmentagencyfor
testingperspective employees.The employmentselectiontestusedhashistoricallyresultedin
scoresof normallydistributedaboutameanof 82 and a standard deviationof 8.A competitor
has developedanewpsychoanalytictestthatitclaimsto be quickerandeasiertoadminister
and therefore lessexpensive. The competitorclaimsthatitstestresultsare the same as those
obtainedbythe reputable agencytest.Manyof the large companies,facingthe financial crunch,
are consideringachange tocut costs.However,theyare unwillingtochange if the competitor
firm’stestresultshave adifferentmeanvalue.Anindependenttestingfirmtested36
prospective employeeswiththe Browntest.A sample meanof 70 resulted.Determine the p
value associatedwiththishypothesistest.(Assume populationstandarddeviationtobe 8).
(5 marks)
Question3:
On a popularself-image testthatresultsinnormallydistributedscores,the meanscore for
public-assistance recipientsisexpectedtobe 65. A random sample of 28 public assistance
recipientsinNTGisgiventhe test.Theyachieve ameanscore of 62.1, and theirscoreshave a
standarddeviationof 5.83. Do the NTG publicassistance recipientstestdifferentlyonaverage,
than whatis expected,atthe 0.02 level of significance?
(http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved
=0CB0QFjAA&url=ftp%3A%2F%2Fmath.uprag.edu%2Fwmartinez%2FJElemStat11%2FChapter9%
2FJElemStat11_09_01.ppt&ei=TXBYVaHvEYySuASMiIDgCw&usg=AFQjCNE_0w94wNXrgr2iO65R
OPnsKhuxhg&sig2=m9MCwBXQmxDxgaNj0oMQbA&bvm=bv.93564037,d.c2E)
(5 marks)
Question 4:
College studentshave regularlyinsistedonfreedomof choice whentheyregisterfortutorial
classes.Inone semesterthere were seventutorialsofferedatdifferenttimesinthe Decision
makingunit.Table belowprovidesthe numberof studentswhoselectedeachof the seven
tutorial classes:
Tutorial 1 2 3 4 5 6 7 Total
No.of
Students
18 12 25 23 8 19 14 119
3. 3
Doesthe data indicate thatstudentshave a preferenceforcertain tutorialsordotheyindicate
that eachtutorial wasequallylikelytobe chosen?Explainyouranswerfully.Show all your
workingsclearly.
(10 marks)
Question5:
Suppose youmove toanothercityaftergraduationto take up a new job.You will,of course,be
concernedaboutthe problemsyouwill face commutingtoandfrom work.You wouldlike to
know,forexample,howlongyouwill ittake youtodrive towork each morning.Using“one way
distance towork” as a measure of where youlive,youremployerhascollectedthe following
data basedon fifteen(15) of the employeesinthe company.Fifteenof yourpotentialcoworkers
have giventhe followingdataof one-waytravel timeanddistancestowork.
Data on Commute DistancesandTime
Coworker Distance in Kilometers Time to travel in minutes
1 3 7
2 5 20
3 7 20
4 8 15
5 10 25
6 11 17
7 12 20
8 12 35
9 13 26
10 15 25
11 15 35
12 16 32
13 18 44
14 19 37
15 20 45
(a) Findthe line of bestfitand the variance of Y about the line of bestfit.Explaininyourwords
whatdo these calculationsindicate.
(b) Findthe 95% confidence interval forthe populationslope.
(c) Is the line of bestfituseful inmakingadecisionthatone-waydistance is suitable in
indicatingone-waytravel time?
(d) Constructa 95% confidence interval forthe meantravel time forthe coworkerswhotravel 7
Kilometers towork.
