bài tập QUẢN TRỊ RA QUYẾT ĐỊNH e

1 QUẢN TRỊ RA QUYẾT ĐỊNH Use suitable statistics to describe and comment about variables Using statistics software MegaStat/Descriptive Statistics, creating a box graph of variables to test check the symmetry of these variables as well as to see which variables may appear values or not, we have followed result: Descriptive statistics Full-time Enrollment Local Tuition ($) Foreign Tuition ($) Age % Foreign Starting Salary ($) count 25 25 25 25 25 25 mean 165.16 12,374.92 16,581.80 28.36 28.08 37,292.00 sample variance 19,836.22 60,503,871.83 83,445,411.67 14.32 625.43 550,336,600.00 sample standard deviation 140.84 7,778.42 9,134.85 3.78 25.01 23,459.25 minimum 12 1000 1000 22 7000 maximum 463 33060 33060 37 90 87000 range 451 32060 32060 15 90 80000 44.00 6,146.00 9,000.00 25.00 6.00 16,000.00 median 126.00 11,513.00 17,765.00 29.00 27.00 41,400.00 3rd quartile 240.00 17,172.00 22,500.00 30.00 43.00 52,500.00 Inter-quartile range 196.00 11,026.00 13,500.00 5.00 37.00 36,500.00 #N/A 16,000.00 29.00 0.00 7,500.00 1st quartile mode 30.00 8/8/2012 21:48.25 (6) The result shows us: Indicators X3 X4 X5 Y 165.16 12,374.92 16,581.80 28.36 28.08 37,292.00 variable 140.84 7,778.42 9,134.85 3.78 25.01 23,459.25 Median (Me) 126.00 11,513.00 17,765.00 29.00 27.00 41,400.00 Mode (M0) 30.00 #N/A 16,000.00 29.00 0.00 7,500.00 First quartile (Q1) 44.00 6,146.00 9,000.00 25.00 6.00 16,000.00 Third quartile (Q3) 240.00 17,172.00 22,500.00 30.00 43.00 52,500.00 Average value of variable X1 X2 Standard deviation of  Conclusion: Basing on the results of statistics and box graph, we have conclusions about - variables: Variable X1 (number of full-time student) is asymmetric and skewed to the right Variables which have values higher than 126 (number of student) account for more - proportion and the data is scattered in the box graph Variable X2 (tuition of indegenous student) is quite symmetric but still skewed a little to the right Variables which have values higher than 11,513 ($) account for more proportion - and the data is scattered in the box graph Variable X3 (tuition of foreign student) is not symmetric and skewed to the left Variables which have values smaller than 17,765 ($) account more and the data is scattered in the - box Variable X4 (average age of student) is not symmetric but skewed to the left Variables which have values smaller than 29 (age) account more and data is scattered in the box graph - Variable X5 (proportion of foreign student) is distributed symmetrically, but quite skewed to the left Variables which have values smaller than 27 (%) account more and the data is - scattered in the box graph Variable Y (starting salary) is asymmetric and skewed to the left Variables which have value smaller than 41,400 ($) account more and the data is scattered in the box Find confidence interval for the rate of courses which require GMAT and English test Using MegaStat/Hypothesis Tests/Compare Two Independent Proportions, we have the followed result: Hypothesis test for two independent proportions p1 p2 pc 0.56 0.32 0.44 p (as decimal) 14/25 8/25 22/50 p (as fraction) 14 22 X 25 25 50 n 0.24 0.1404 1.71 0874 difference hypothesized difference std error z p-value (two-tailed) -0.027 confidence interval 95.% lower 0.507 confidence interval 95.% upper 0.267 margin of error  Conclusion: Confidence interval for courses which require GMAT and english test is from -0.027 to 0.507 4 Find confidence interval for average starting salary of MBA graduates from these courses Using MegaStat/Descriptive Statistics, we have followed resutl: Descriptive statistics Starting Salary ($) count 25 mean 37,292.00 sample variance 550,336,600.00 sample standard deviation 23,459.25 minimum 7000 maximum 87000 range 80000 confidence interval 95.% lower 27,608.50 confidence interval 95.% upper 46,975.50 half-width 9,683.50  Conclusion: Confidence interval for average starting salary of MBA graduates from these courses is from 27,608.50 to 46,975.50 Test the hypothesis about the equation of average tuition between foreign and indigenous students Using MegaStat/Hypothesis Tests/Paired Observations, we have the followed result : Hypothesis Test: Paired Observations 0.000 hypothesized value 12,374.920 mean Local Tuition ($) 16,581.800 mean Foreign Tuition ($) -4,206.880 mean difference (Local Tuition ($) - Foreign Tuition ($)) 5,032.353 std dev 1,006.471 std error 25 n 24 df -4.18 t 0003 p-value (two-tailed) -6,284.133 confidence interval 95.% lower -2,129.627 confidence interval 95.% upper 2,077.253 margin of error Test the couple of hypotheses: H0: µ1 = µ2 (average tuition of indigenous and foreign students is equal) H1: µ1 ≠ µ2 (average tuition of indigenous and foreign students is different) We have p-value = 0.0003 which is smaller than significance level α = 0.05 (5%), thus, reject the hypothesis H0 and accept the hypothesis H1, or µ1 ≠ µ2  Conclusion: Average tuition of indigenous and foreign students is different Test the difference in starting salary between courses which require English test and which not require English test Using MegaStat/Hypothesis Tests/Compare Two Independent Groups, we have the followed result: Hypothesis Test: Independent Groups (t-test, pooled variance) Starting Salary with English Starting Salary without English 45,087.50 33,623.53 mean 21,026.54 24,236.25 std dev 17 n 23 df 11,463.971 difference (Starting Salary with English - Starting Salary without English) 543,179,971.228 pooled variance 23,306.222 pooled std dev 9,992.460 standard error of difference hypothesized difference 1.15 2631 t p-value (two-tailed) F-test for equality of variance 587,395,661.76 variance: Starting Salary without English 442,115,535.71 variance: Starting Salary with English 1.33 F 7338 p-value Test the couple of hypotheses: H0: µ1 = µ2 (there is no difference between courses) H1: µ1 ≠ µ2 (there is a difference between courses) We have t = 1.15, corresponding to p-value = 0.2631 much larger than significance level α = 0.05 (5%), thus reject the hypothesis H0  Conclusion: Statistically, there is no significant difference in starting salary between courses Estimate the regression model in which dependent variable is starting salary, independent variables are remaining quantitative variables: a Which independent variables are important in the model? The sign of regression coefficient is suitable with your expectation? Use alpha = 5% Using MegaStat/Correlation-Regression/Regression Analysis, we have followed result : Regression Analysis R² 0.741 Adjusted R² 0.673 n 25 R 0.861 k Std Error 13414.925 Dep Var Starting Salary ($) ANOVA table Source SS df MS F p-value 10.88 4.72E-05 Regression 9,788,834,248.7736 1,957,766,849.7547 Residual 3,419,244,151.2264 19 179,960,218.4856 Total 13,208,078,400.0000 24 Regression output confidence interval variables coefficients std error t (df=19) pvalue 95% lower 95% upper Intercept -51,108.3665 31,139.4732 -1.641 1172 -116,284.0327 14,067.2997 Full-time Enrollment -3.9827 26.9575 -0.148 8841 -60.4055 52.4401 Local Tuition ($) 1.6817 0.8175 2.057 0537 -0.0293 3.3927 Foreign Tuition ($) 0.3223 0.5959 0.541 5949 -0.9249 1.5695 Age 2,210.4618 1,027.9666 2.150 0446 58.9029 4,362.0206 % Foreign 7.6243 149.7357 0.051 9599 -305.7761 321.0247 Regression equation: Y = -51,108.3665–3.9827*X1 + 1.6817*X2 + 0.3223*X3 + 2,210.4618*X4 + 7.6243*X5 In which: X1 number of full-time student X2 tuition of indigenous student X3 tuition of foreign student X4 average age of student X5 proportion of foreign student Y starting salary Independent variables which are significant in the model are: X2, X3, X4, X5 and the sign of regression coefficent is suitable with our expectation b Explain the meaning of regression coefficient and R2 + Coefficient of X1: Assuming that X2, X3, X4, X5 are unchanged: if the number of fulltime student increases by person, the starting salary reduces by 3.9827$ + Coefficient of X2: Assuming that X1, X3, X4, X5 are unchanged: if the tuition of indigenous student increases 1$, the starting salary will increase 1.6817$ + Coefficient of X3: Assuming that X1, X2, X4, X5 are unchanged: if the tuition of foreign student increases 1$, the starting salary will increase 0.3223$ + Coefficient of X4: Assuming that X1, X2, X3, X5 are unchanged: If the average age increases 1, the starting salary will increase 2,210.4618$ + Coefficient of X5: Assuming that X1, X2, X3, X4 are unchanged: if the proportion of foreign student increases by 1%, the starting salary will go up by 7.6243$ R2 = 0.741 means that 74.1% change of starting salary is due to independent variables X1, X2, X3, X4, X5, remaining 25.9% is because of other factors c Test the suitability of the regression model and explain the meaning Test the hypothesis: H0: β1 = β2 = β3 = β4 = β5 = (all factors have no influence) H1: at least one coefficient β ≠ Look at Anova Table, we have F = 10.88, F value is quite high, showing that valued parts of the model have much influence We have: p-value = 4.72E-05 very small, smaller than α = 0.05 (5%), thus reject the hypothesis H0 and accept the hypothesis H1  Conclusion: There is at least one factor or all five factors affect to the starting salary 10 d Forecast the starting salary if independent variables from X1 to X5 respectively take values (250, 20500, 20500, 26,40) Using statistics software MegaStat/Correlation-Regression/Regression Analysis, choose Type in predictor values, we have the followed result: Predicted values for: Starting Salary ($) 95% Confidence Interval 95% Prediction Interval Full-time Enrollment Local Tuition ($) Foreign Tuition ($) Age % Foreign Predicted lower upper lower upper Leverage 250 20,500 20,500 26 40 46,755.144 34,867.347 58,642.941 16,264.483 77,245.805 0.179 In the table, the starting salary is 46,755.144 USD with confidence interval from 34,867.347 to 58,642.941 Conclusion: If the number of full-time student is 250; tuition for indigenous student is 20,500; tuition for foreign student is 20,500; average age of students is 26 and the proportion of foreign students is 40%, the starting salary ranges between 34,867.347 58,642.941 USD with probability of 95% 11 ... significant difference in starting salary between courses Estimate the regression model in which dependent variable is starting salary, independent variables are remaining quantitative variables: a Which... which not require English test Using MegaStat/Hypothesis Tests/Compare Two Independent Groups, we have the followed result: Hypothesis Test: Independent Groups (t-test, pooled variance) Starting... accept the hypothesis H1, or µ1 ≠ µ2  Conclusion: Average tuition of indigenous and foreign students is different Test the difference in starting salary between courses which require English test