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Business StatisticsNameInstitutionInstructor22nd September 2017Allocated sample number: 1071
Section 1Use the dataset given below you must use the sample allocated to you based on your studentnumberhttps://app.box.com/s/56pb6hqu0ypcg0f3lhy6cl5szt1jgdlaNote that for section 1 the answers are provided so you can check your work, the answers willnot be provided for the other sections. A)paste in the scatterplot for your sample into your word document and give a simplecomment about the relationship between the variables, (you do not need to submit theexcel file) SolutionAs can be seen in the above plot, there is a positive linear relationship between incomeand annual contribution. An increase in income results to an increase in annualcontribution while a decrease in income results to a decrease in annual contribution.B)Estimate the annual contribution if the income is \$200,000 using the regression line frompart (a) SolutionThe regression equation is given as follows;Annualcontribution=1258.9+0.1183IncomeNow with an income of \$200,000 we have;Annualcontribution=1258.9+0.1183(200000)Annualcontribution=\$24918.9C)Find the z-score of the estimate in part (B) note that average of the estimates is \$27,000with standard deviation \$2,100, remember to show your work. Solutionzscore= ́xμσ=24918.9270002100=0.991D)using the z-score from part (C) Find P(Z<z-score) , you can find out the answer usingwww.wolframalpha.com2
for example found the z-score was 1.5 if the z-score is 1.5 type in P(Z<1.5) into wolfram alpha.comSolutionP(Z<zscore)=P(Z0.991)=0.1608E)If there was a list of 10,000 estimates ranked from lowest to highest, what rank do youthinkyourestimatewouldbecloseto?Hint:justusetheformulaexpected rank = P(Z<z-score)*10000, remember to show your work. SolutionExpectedrank=P(Z<zscore)10000Expectedrank=0.160810000=1608Section2Use the dataset given below you must use the sample allocated to you based on your studentnumberhttps://app.box.com/s/yvhk3e3oymbs3toy6j5xetid82dsjyz4A)Use the PivotTable feature in excel to find appropriate summary statistics for yoursample, This will probably require two PivotTables. You should paste both into word,you do not need the excel file. Make sure the pivot table (or pivot tables) include the following statistics *Just considering the high risk (riskier type) investments what is the sample size n1andthe proportion of high risk investments that made a loss ^p1*Just considering the low risk (safer type) investments what is the sample size =n2andWhat is the proportion of low risk investments that made a loss ^p2SolutionCount of made a loss (L or P)?Column LabelsRow LabelsLPGrand Totalr195675s12425Grand Total2080100High risk investmentSample size n1 is 75 Proportion that made a loss ^p1is 1975=0.2533Low risk investments, Sample size n2 is 25Proportion that made a loss ^p2is 125=0.043
B)Use excel to make an appropriate graph that lets you compare the proportions found inparts A and paste this into your word document SolutionC)Looking at your answers to parts (A) and (B) Make a simple comment about therelationship betweenthevariablesinvestmenttype(riskorsafe)andMade a profit (madea profit/made a loss) SolutionClearly a huge proportion (96%) of safer investments made profits as compared to riskierinvestments (74.7%)D)Questionsi)Using your sample what is the estimate for p1- p2? In other words what is thedifference between the sample proportions ^p1 -^p2Solution^p1^p2¿0.25330.04=0.2133ii)Find the z-score of the estimate in part (i) note that average of the estimates is 0.1with standard deviation 0.0743Solution0.21330.1(10.1)(175+125)=3.0787iii)Usingpart(ii)findP(Z<z-score)usingwww.wolframalpha.comfor example ifthe z-score is 0.5 typeinP(Z<0.5)” into wolframalpha.comSolutionP(Z<3.0787)=0.99904

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