Business Statistics: Assignment (Doc)
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Added on 2020-03-23
Business Statistics: Assignment (Doc)
Added on 2020-03-23
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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) Solution Figure 1: Scatter plot of annual income versus annual contributionFigure 1 above shows that there exists a linear positive relationship between annualincome and annual contribution. As the annual income increase so does the annualcontribution. Likewise, as the annual income decreases so does the 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;Annual contribution = -7936.9+0.173*IncomeNow with an income of $200,000 we have;Annual contribution = -7936.9+0.173*(200000)Annual contribution=$26,663.1C)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= ́x−μσ=26663.1−270002100=−0.1604D)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(Z<−0.1604)=0.4363E)If there was a list of 10,000 estimates ranked from lowest to highest, what rank do youthinkyourestimatewouldbecloseto?Hint:justusetheformulaexpected rank = P(Z<zscore)*10000, remember to show your work. SolutionExpectedrank=P(Z<zscore)∗10000Expectedrank=0.4363∗10000=4363Section2Use 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 Totalr185573s72027Grand Total2575100The sample size for high risk investment, n1 is 73 while the proportion of high riskinvestments that made a loss ^p1is 1873=0.2466The sample size for low risk investment, n2 is 30 while the proportion of low riskinvestments that made a loss ^p2is 727=0.25933
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) SolutionAs can be seen, a slightly high proportion (75%) of higher risk investments made profitscompared to the 74% of safer risk investments that made profitsD)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¿0.2466−0.2593=−0.0127ii)Find the z-score of the estimate in part (i) note that average of the estimates is 0.1with standard deviation 0.0743Solution−0.0127√0.1(1−0.1)(173+127)=−0.0649iii)Usingpart(ii)findP(Z<z-score)usingwww.wolframalpha.comfor example ifthe z-score is 0.5 typeinP(Z<0.5)” into wolframalpha.com4
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