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Posted: July 24th, 2023

THE UNIVERSITY RESERVES THE RIGHT NOT TO MARK YOUR

BUS105eSpecimen Examination PaperStatistics____________________________________________________________________________________Time allowed: 2 hours____________________________________________________________________________________INSTRUCTIONS TO STUDENTS:1. This examination contains FOUR (4) questions and comprises SEVENTEEN(17) printed pages (including cover page).2. You must answer ALL questions.3. All answers must be written in the answer book.4. Appendices are attached from Page 10 to 17 of this examination paper.At the end of the examinationPlease ensure that you have written your examination number on each answer bookused.Failure to do so will mean that your work cannot be identified.If you have used more than one answer book, please tie them together with the stringprovided.THE UNIVERSITY RESERVES THE RIGHT NOT TO MARK YOURSCRIPT IF YOU FAIL TO FOLLOW THESE INSTRUCTIONS.BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 1 of 17You must answer ALL the questions. (Total 100 marks)Question 1Refer to Appendix A1 and Appendix A2 for this part of the question.China and Chile are some of the more earthquake-prone countries in the world. Thehighest number of fatalities from an earthquake was recorded in China while thestrongest earthquake ever measured occurred in Chile.Earthquake magnitudes are measured on the Richter scale as shown below:Figure 1(a)Describe the highest number of earthquake fatalities that are recorded in thedata for China and Chile. Describe the earthquakes when these fatalitiesoccurred.(6 marks)(b)How accurate do you think are the fatalities recorded? Why do you think so?(6 marks)BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 2 of 17(c)The chart below (Figure 2) is obtained from the Chilean earthquake data byassuming that entries that do not list fatalities have zero fatality.Name the type of this statistical chart and describe what the chart says aboutearthquakes in Chile.Figure 2(6 marks)BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 3 of 17(d)The data for China (excepting the first entry which does not have a magnituderecorded) is processed on the Excel spreadsheet as shown below (Figure 3). Onthe left, the magnitude data has been sorted. On the right, the histogram hasbeen created with the data analysis tools.Write down the class intervals for the histogram and comment on the shape ofthe histogram with reference to earthquake occurrences in China.Figure 3(7 marks)Question 2(a)It is reported that Singaporeâs population by ethnic group in 2013 has thefollowing composition by relative frequencies:Ethnic GroupChineseMalayIndianOthers(i)Percentage74.2%13.3%9.1%3.4%Verify that the relative frequencies shown here can be interpreted as alegitimate assignment of probabilities for the 4 outcomes when selectinga Singaporean randomly and inspecting his/her ethnicity.BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 4 of 17(b)(ii)Identify the probability that a randomly chosen Singaporean is Malay orIndian.(iii)Identify the probability that a randomly chosen Singapore is notcategorised as âOthersâ.(9 marks)Annual sales, in thousands of dollars, for 40 technology companies are inColumns A and B while the descriptive statistics computed using Excelâs dataanalysis tools are found in the range D1:E15 as shown below:(i)Assuming that the sample statistics are good approximates of thepopulation statistics and that the annual sales of technology companiesare distributed according to the normal distribution. Write down thevalue x where x is 2 standard deviations larger than the mean andestimate the probability that the sales figure of a randomly chosentechnology company is larger than x.(8 marks)(ii)Without assuming that the annual sales of technology companies aredistributed according to the normal distribution, estimate the probabilitythat the sample mean is larger than $6,000 thousand. Justify youranswer.(8 marks)BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 5 of 17Question 3Mr Nelson Limâs family business manufactures iron rods. Recently, he upgraded hisrod casting machine to the latest high speed model. However, he has noticed that theamount of raw iron consumed has increased even though the machine is tuned toproduce rods at the length of 1 metre. Suspicious that the machine setting of 1 metre isnot functioning properly, Mr Lim noted down the lengths of 40 rods with the aim todetermine statistically if it is indeed so.He created a statistical report with Excel as shown here:The data in the range A1:D10 record the lengths of the rods that were sampled. Thetable in columns F and G is produced by the Descriptive Statistics function of the dataanalysis tools.(a)(b)Mr Lim would like to use confidence intervals to investigate his suspicions.(i)State the 95% confidence interval for the mean rod length. Interpret thisconfidence interval with respect to Mr Limâs suspicion.(ii)Discuss the key assumption(s) you have made in your construction ofthe confidence interval.(iii)Discuss the factors that affect the width of the confidence interval.Explain the effects of increasing or decreasing these factors.(15 marks)Mr Lim would like to conduct a test of hypothesis on the same dataset so that hemay gain an alternative perspective. He created the following report using Exceldata analysis tools, setting the parameter Alpha to 0.05:BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 6 of 17Select a suitable test of hypothesis at the 5% level of significance to determineif the mean of the lengths of the rods that are produced by the new rod castingmachine is equal to 1. You are required to show the detailed steps and theappropriate test statistic in conducting the test.(10 marks)Question 4A major portion of Cranberry Food Delivery Pte Ltd involves delivering lunch boxes toits customers. In order to schedule the deliveries efficiently, the managers needed toestimate the total travel time for the drivers of the company on assignments which arecarried out in the day.It is deemed that the daily total travel time is dependent on the km travel (i.e. distancetravelled in km) as well as the number of delivery stops. Data is thereby collected anddisplayed in the following diagram:BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 7 of 17Multiple regression analysis is applied on Excel to produce the following report:Reading from the report, answer the following questions:(a)Describe the linear relationship underlying the data by writing down the linearequation that relates the Total Travel Time to the Number of Deliveries and kmTravelled. Interpret the coefficients obtained as they relate to the managersâscheduling problem.(4 marks)(b)State the coefficient of determination and the adjusted coefficient ofdetermination. Interpret them and explain how they are different from eachother.(4 marks)(c)A new route is planned on which there will be 3 delivery stops and the length ofthe route is 85 km. Estimate the total travel time in hours.(4 marks)(d)Conduct a global test of hypothesis on the regression model at the 5%significance level to investigate whether or not all the independent variableshave zero regression coefficients. Lay down your steps carefully.(6 marks)BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 8 of 17(e)What are the assumptions made when the method of regression is applied tostudy data? Discuss these assumptions in the context of the delivery schedulingproblem of Cranberry Food Delivery Pte Ltd.(7 marks)----- END OF PAPER -----BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 9 of 17Appendix A1Source: U.S. Geological SurveyBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 10 of 17Appendix A2Source: U.S. Geological SurveyBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 11 of 17Appendix B: TablesSource:Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. &Wathen, Samuel A. (2012) 8th Edition, McGraw-HillBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 12 of 17BUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 13 of 17Source:Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. &Wathen, Samuel A. (2012) 8th Edition, McGraw-HillBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 14 of 17Source:Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. &Wathen, Samuel A. (2012) 8th Edition, McGraw-HillBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 15 of 17Source:Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. &Wathen, Samuel A. (2012) 8th Edition, McGraw-HillBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 16 of 17Source:Basic Statistics for Business & Economics by Lind Douglas A., Marchal William G. &Wathen, Samuel A. (2012) 8th Edition, McGraw-HillBUS105e Copyright Â© 2015 SIM UniversitySpecimen Examination PaperPage 17 of 17

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