MATH1068 -Statistical Methods Assessment

Instructions

• Thisassignmenthasthreequestions,eachassociatedwithaspecialdataAlldatafilesneededforthisassignmentareintheAssignmentTabfolder.ThefilesareinExcelformatandshould be copied directly intoMinitab.
• Thenumberofmarks foreachquestionis displayednexttothe question.
• Itisimportantthatyoufollowanyinstructionsgiveninthequestions,suchasUseMinitabwhere required. It isup to you whetherto use hints or
• RefertotheMinitabguidepostedonthelearnonlinewebsiteinDataFiles&Minitab
• Minitaboutputwillberequiredandtoavoidlosinganyinformationwhenuploaded,your

assignmentfile shouldbesubmitted as asinglePDF document file.

• Submission is online on the learnonline website via special link. Assignments will bemarkedand returned online.
• Late submission without approved extension will attract a penalty of 10% off themaximum marks per every extra day after the due date. The cut-off time is 5pm each

Question1(30Marks)DescribingDistributions

StKildaHousingSalePricesInvestigation.

Inthelastfewyears,thehousingmarkethaschangedsignificantly.Itisimportanttounderstand historical data on sale prices and obtain key insights from pre-Covid era tounderstand current trends. The data used in this investigation was collected in the St Kildasuburb of Melbourne and includes housing sale prices for 368 properties recorded betweenSeptember2016andFebruary2018.Therearetwotypesofhousinginthisdataset:house

(h) and unit (u).The main aim is to analyse and provide some insights on housing sale pricesbeforeCovid-19 pandemic.

atafile:StKildaHousing.csv

• (2marks) UseMinitabtoproduce ahistogramofthePrice($).
• (2marks)UseMinitabto produceDescriptive StatisticsforthePrice($).
• (2marks)UseMinitabtoproduceaboxplotdescribingthePrice($).Showtheboxplothorizontally(Minitabbooklet hasinstructions on howto rotateaboxplot).

• (5marks)Usingyouroutputfrom(a)to(c),commentontheshapeofthedistributionforthePrice ($). In particular,
  • Discusswhetherthereisonepeak,ormultiplepeaksinthedistribution,
  • Describetheshapeofthedistribution(skewedorsymmetric),
  • Determineifthere arethere anyoutliers,
  • Explain, characterise, and give reasons for any irregular patterns in the prices.Hint:Thedistributioncontainsdifferentsetsofpricesfordifferenttypesofhousing,and missing data that has $0 price. Use Minitab to plot the boxplot for eachhousing type (house and unit) prices and compare with your findings for all typesofhousings selling prices done earlier.
• (4marks)UseMinitabtoproduceboxplotsofeachhousetypecategorisedinyouranswerfrom(d) excluding zero-dollar(missing data) prices.Hint: Use thecondition function.
• (5 marks) Use Minitab to produce new Descriptive Statistics summaries of Price ($) foreach type of housing with missing data removed. Which measures of central tendencyand dispersion are the most appropriate to numerically summarise and compare thedifferentsellingpricesforhousesandunits?Forfullmarks,justifyyourchoiceofmeasures and interpret the corresponding values. Hint: Use the sort function and createa newsorted entire dataset.
• (4marks)UseMinitabtoplottheNormalitycurvesforeachhousingtypePrice($),brieflydescribeeachplotanddeterminewhetherthe datafollowsa Normal
• (6marks)Basedontheknowledgeobtainedinpart(g),useMinitabtocalculatetheprobabilitythattheAveragePrice($)ofaHousepropertytypewillbelessthan

$1,400,000.

Question2(30marks)NormalDistribution&CLT

Generating Exam Scores. Recently, a cohort of 100 students of a university statistics coursesat their final examination and their exam scores were recorded. The statistics lecturer isinterested in analysing the data and calculating the probabilities for a student to achieve acertainscoreandinfindinginformation regardingthe average scorefor a cohort.

Datafile:exam.csv

• (5marks)UseMinitabtoproduceahistogramandtheDescriptiveStatisticsfortheexamDescribe the shape ofthedistributionand justify your answer.

• (6marks)CalculatetheprobabilitythatastudentsexamscoreisgreaterthanForfullmarks, show all your working out by hand except a Normality test, provide a correctprobabilitystatement and include theMinitaboutputto verify your answer.
• (5 marks) If a student scores in the top 5% of the cohort, what is the minimum requiredexam score to get into the top 5% of the class? For full marks, show all your working outby hand, provide a correct probability statement, and include the Minitab output toverifyyour answer.
• (4marks)ByusingMinitab,producefiverandomsamplesofsize30byrandomlyselecting 30 values from the exam score dataset. For full marks, provide a screenshot ofeach
• (4 marks) Use Minitab to produce the Descriptive Statistics for each sample. What arethe parameters of the sampling distribution of exam scores based off your first sample?Brieflyjustify your
• (6 marks) Calculate the probability that the average (mean) exam score is less than 75based on your sampling distribution of the means from part (e). You can assume herethatthecohortof100studentsisaForfullmarks,showallyourworkingoutbyhand,provideacorrectprobabilitystatement,andincludeallMinitaboutputsupportingyouranswer.

Question3(25marks)ConfidenceIntervals

Analysing data on Fuel Efficiency: Fuel efficiency (in liters per 100 km) is one of the mostimportantparameterswelookatwhenchoosingtobuyanewcar.Acarreviewerisinterestedto find out the average fuel efficiency on highways for modern cars with engine capacity of2Landreportittothenewbuyersinhisblog.Heteststheefficiencyfor79carswhiledrivingthemonthesamehighway.Investigateandanalysethedataobtainedbythecarreviewertofind out an average fuel consumption on highways for modern cars with engine capacity of2L.

Datafile:fuel.csv

• (2marks)UseMinitabtoproduceahistogramoftheFuelConsumption(L/100km).
• (2marks)UseMinitabtoproduceDescriptiveStatisticsfortheFuelConsumption(L/100km).Identify the sample standard deviation.
• (4marks)CommentontheshapeofthedistributionandtestthedistributionforWoulditbereasonabletoconstructaconfidenceintervalforthepopulation

meanfuelconsumptionbasedontheNormaldistributionusingthisdataset?Explainyouranswer.

• (6 marks) Construct and interpret the 99% confidence interval for the population meanfuel consumption based on the sample data. All calculations should be done manuallywithoutusingMinitab,however,you canuseMinitabto visualiseandverifythe results.
• (4 marks) Repeat part (d) for the 95% confidence interval for the population mean fuel
• (2marks)Thecarmakerswebsiteclaimsthattheaverage(mean)FuelConsumptionfortheir 2L engine cars is 7.1L per 100km. Discuss whether this claim is valid using 95%confidenceintervalandthen99% confidenceWhatconclusionscan bemade?
• (5 marks) The car maker would prefer to update their claim and focus on specifying themarginoferrortobewithin75%ofthestandarddeviationand95%confidence.Whatwouldbetheapproximaterequiredsamplesizetomakethispossible?Discussthisresult.