4 marks question 5 a management consulting company

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(4 marks)Question 5A management consulting company presents a 3-day seminar on project management tovarious clients. The seminar is basically the same each time it is given. However, sometimesit is presented to high-level managers, sometimes to mid-level managers and sometimes tolow-level managers. The seminar organizers believe evaluations of the seminar may varywith the audience. Suppose the following data are random scores for seminar attendees.QUESTIONS CONTINUE OVER PAGE
Semester One Final Examinations, 2018ECON7300 Statistics for Business and EconomicsPage 9 of 25High-levelMid-levelLow-level7857968837102991Sum = 38Mean = 7.6Sum = 44Mean = 8.8Sum = 17Mean = 3.4The partially completed ANOVA summary table is as follows:ANOVASource of variationSum of squaresDegrees of freedomBetween groups80.4Within groupsTotal103.6A.Can we conclude at the 5% significance level that there are differences in the averagescores for the different levels of managers? Follow all the necessary steps to perform thetest.(4 marks)B.Based on the results of the test in (A.), use the Tukey-Kramer method (if warranted) with5% level of significance to determine which of the group means are significantly different.(4 marks)Question 6Background: During South Africa’s apartheid regime (1948-1994), individuals were officiallyclassified into one of four racial groups: “Asian”, “Black”, “Coloured” and “White”.Although the apartheid policy has long been abolished, it is still widely believed that the racialgroup a person belongs to plays a substantial role in determining employment outcomes andearnings in South Africa today.QUESTIONS CONTINUE OVER PAGE
Semester One Final Examinations, 2018ECON7300 Statistics for Business and EconomicsPage 10 of 25The following linear regression model was estimated using the nationally-representativeSouth African survey data.Dependent variable:Income= Household income (Rand per month)Independent variable:White= 1 if the household head is a white South African; 0 otherwiseThe regression output is shown below.SUMMARY OUTPUTRegression StatisticsMultiple R0.388861R Square0.151213Adjusted R Square0.15118Standard Error2989.824Observations25965ANOVAdfSSMSFSignificance FRegression14.13E+104.13E+104625.341Residual259632.32E+118939048Total259642.73E+11CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept1509.27619.9065275.8181701470.2581548.294White3737.44954.9545268.0098603629.7353845.163A.Interpret BOTH the estimated coefficients.0(2 marks)B.Interpret the ‘Lower 95%’ and ‘Upper 95%’ columns forWhite.(1 mark)C.Perform a test for a difference in mean household income according to race. Use acritical value approach.(2 marks)D.Explain how you already knew the result of this test in (C) based on your answer to (B).(2 marks)Now suppose we add some explanatory variables to the model:Asian=1 if the household head is an Asian South African; 0 otherwiseColoured= 1 if the household head is a coloured South African; 0 otherwiseYears of Education= Years of education of the household headAge= Age of the household head, in yearsAge Squared= Age squaredQUESTIONS CONTINUE OVER PAGE
Semester One Final Examinations, 2018ECON7300 Statistics for Business and EconomicsPage 11 of 25SUMMARY OUTPUTRegression StatisticsMultiple R0.438882R Square0.192617Adjusted R Square0.192431Standard Error2985.349Observations25965ANOVAdfSSMSF

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Economics, Regression Analysis, Lecturer, Final Examinations

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