namibia UniVERSITY OF SCIEnCE AnD TECHnOLOGY FACULTY OF HEALTH AND APPLIED SCIENCES DEPARTMENT OF MATHEMATICS AND STATISTICS QUALIFICATION: BACHELOR OF ECONOMICS -., QUALIFICATION CODE: 7BAMS LEVEL: 7 COURSE CODE: SFE612S COURSE NAME: STATISTICS FOR ECONOMISTS SESSION: NOVEMBER 216 DURATION: 3 HOURS PAPER: THEORY MARKS: 1 EXAMINERS: FIRST OPPORTUNITY EXAMINATION MR O.P.L. MTAMBO, MR C. MAPIRA, MR D. NTIRAMPEBA MODERATOR: MRA. ROUX INSTRUCTIONS 1. Answer ALL the questions in the booklet provided. 2. Show clearly all the steps used in the calculations. 3. All written work must be done in blue or black ink and sketches must be done in pencil. PERMISSIBLE MATERIALS 1. Non-programmable calculator without a cover. 2. Attached statistical tables. THIS QUESTION PAPER CONSISTS OF 4 PAGES {Including this front page} Page 1 of4
QUESTION 1 [1 Marks] A gambler is testing an octahedral die in order to determine if it is fair or not. She rolls it 8 times and observes the following results. Score 1 2 3 4 5 6 7 8 Frequency 7 1 11 9 12 1 14 7 Test, at 1% level of significance, whether the die is fair for a gambling game. [1] QUESTION 2 [15 Marks] A researcher is interested in predicting value of variable y given the value of variable x. Suppose that she has observed the data given in the table below. X 4 5 6 7 8 9 y 54 33 2 13 85 52 One best fitting regression model for these data is a simple non linear model of the form y = abx where a and b are constants. 2.1 Transform the given simple nonlinear model into a simple linear model. [2] 2.2 Use the ordinary least square {OLS) method to fit simple linear model obtained in 2.1. [All transformed data must be rounded to 2 decimal places] [1] 2.3 Use the fitted model in 2.2 to predict the value of y when x = 6.4 correct to 1 decimal place. [3] QUESTION 3 [2 Marks] The principal wishes to determine whether the final mark of a student in Mathematics is affected by his or her marital status controlling for his or her gender. The following final marks in Statistics are scored. Page 2 of 4
Marital status Gender Male Female Total Single 92 9 182 Married 82 66 148 Divorced 67 61 128 Widowed 51 59 11 Total 292 276 568 3.1 Construct an appropriate two-factor ANOVA table for these data. [11] 3.2 Determine whether the final mark of a student in Mathematics is affected by marital status and/or gender of the student at 5% level. [9] QUESTION 4 [25 Marks) 4.1 State any 4 assumptions of a multiple linear regression model. [4] 4.2 A researcher wishes to build an appropriate multiple linear model for predicting response variable Y using three predictor variables X 11 X 2, and X 3. She has just made fourteen observations and analysed her data using SPSS. Part of her analysis outputs is as given in the table below. U nstandardized Standardized Coefficients Coefficients Model B Std. Error Beta t 1 (Constant) 58.69 18.485 Xl 2.686 1.244.457 X2 -.68 1.179 -.14 X3-3.185 1.6 -.557 (a) Use her model to predict the outcome when X 1 = 1, X 2 = 12, and X 3 = 15. [2] (b) Construct the ANOVA table given that SSR = 5959.365 and that MSE = 7.635. [4] (c) Compute the adjusted multiple coefficient of determination and interpret it. [3] (d) Test for overall adequacy of the fitted model at 1% level? [4] (e) Compute all observed t-values and hence determine all significant predictors, if any, of Y at 1% level. [8] Page 3 of4
QUESTION 5 [3 Marks] The quarterly cotton yields (in tons) for KHY cotton farm were recorded for the years 213 to 215 as in the table below. Quarter Year 213 214 215 1 32 25 32 2 42 45 44 3 62 62 82 4 3 35 78 5.1 Compute the 4-period centered moving average and the seasonal ratios for these quarterly cotton yields. [12] 5.2 Compute the adjusted seasonal indexes for these quarterly cotton yields. [1] 5.3 5.4 Compute the de-seasonalised quarterly cotton yields. Interpret the de-seasonalised l 5 t quarter cotton yield for 215. [6] [2] END OF QUESTION PAPER Page 4 of4
t-distribution Table /\ ~ t The shaded area is equal to a fort= ta.!.too t.oso t.25 t.oto t.oos 1 3.78 6.314 12.76 31.821 63.657 2 1.886 2.92 4.33 6.965 9.925 3 1.638 2.353 3.182 4.541 5.841 4 1.533 2.132 2.776 3.747 4.64 5 1.476 2.15 2.571 3.365 4.32 6 1.44 1.943 2.447 3.143 3.77 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.86 2.36 2.896 3.355 9 1.383 1.833 2.262 2.821 3.25 1 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.21 2.718 3.16 12 1.356 1.782 2.179 2.681 3.55 13 1.35 1.771 2.16 2.65 3.12 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.62 2.947 16 1.337 1.746 2.12 2.583 2.921 17 1.333 1.74 2.11 2.567 2.898 18 1.33 1.734 2.11 2.552 2.878 19 1.328 1.729 2.93 2.539 2.861 2 1.325 1.725 2.86 2.528 2.845 21 1.323 1.721 2.8 2.518 2.831 22 1.321 1.717 2.74 2.58 2.819 23 1.319 1.714 2.69 2.5 2.87 24 1.318 1.711 2.64 2.492 2.797 25 1.316 1.78 2.6 2.485 2.787 26 1.315 1.76 2.56 2.479 2.779 27 1.314 1.73 2.52 2.473 2.771 28 1.313 1.71 2.48 2.467 2.763 29 1.311 1.699 2.45 2.462 2.756 3 1.31 1.697 2.42 2.457 2.75 32 1.39 1.694 2.37 2.449 2.738 34 1.37 1.691 2.32 2.441 2.728 36 1.36 1.688 2.28 2.434 2.719 38 1.34 1.686 2.24 2.429 2.712 1.282 1.645 1.96 2.326 2.576 Gillcs Cazclais. Typeset with k\tex on Apri12, 26.
Chi-Square Distribution Table The shaded area is equal to ex for x 2 = x;. df X~ggs X 2 ggo X 2 975 X~gso X 2 goo X~wo X 2 oso X 2 o2s X~o1 x:oos 1...4.16 2.76 3.841 5.24 6.635 7.879 2.2.51.13.211 4.65 5.991 7.378 9.21 1.597 3.72.115.216.352.584 6.251 7.815 9.348 11.345 12.838 4.27.297.484.711 1.64 7.779 9.488 11.143 13.277 14.86 5.412.554.831 1.145 1.61 9.236 11.7 12.833 15.86 16.75 6.676.872 1.237 1.635 2.24 1.645 12.592 14.449 16.812 18.548 7.989 1.239 1.69 2.167 2.833 12.17 14.67 16.13 18.475 2.278 8 1.344 1.646 2.18 2.733 3.49 13.362 15.57 17.535 2.9 21.955 9 1.735 2.88 2.7 3.325 4.168 14.684 16.919 19.23 21.666 23.589 1 2.156 2.558 3.247 3.94 4.865 15.987 18.37 2.483 23.29 25.188 11 2.63 3.53 3.816 4.575 5.578 17.275 19.675 21.92 24.725 26.757 12 3.74 3.571 4.44 5.226 6.34 18.549 21.26 23.337 26.217 28.3 13 3.565 4.17 5.9 5.892 7.42 19.812 22.362 24.736 27.688 29.819 14 4.75 4.66 5.629 6.571 7.79 21.64 23.685 26.119 29.141 31.319 15 4.61 5.229 6.262 7.261 8.547 22.37 24.996 27.488 3.578 32.81 16 5.142 5.812 6.98 7.962 9.312 23.542 26.296 28.845 32. 34.267 17 5.697 6.48 7.564 8.672 1.85 24.769 27.587 3.191 33.49 35.718 18 6.265 7.15 8.231 9.39 1.865 25.989 28.869 31.526 34.85 37.156 19 6.844 7.633 8.97 1.117 11.651 27.24 3.144 32.852 36.191 38.582 2 7.434 8.26 9.591 1.851 12.443 28.412 31.41 34.17 37.566 39.997 21 8.34 8.897 1.283 11.591 13.24 29.615 32.671 35.479 38.932 41.41 22 8.643 9.542 1.982 12.338 14.41 3.813 33.924 36.781 4.289 42.796 23 9.26 1.196 11.689 13.91 14.848 32.7 35.172 38.76 41.638 44.181 24 9.886 1.856 12.41 13.848 15.659 33.196 36.415 39.364 42.98 45.559 25 1.52 11.524 13.12 14.611 16.473 34.382 37.652 4.646 44.314 46.928 26 11.16 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.29 27 11.88 12.879 14.573 16.151 18.114 36.741 4.113 43.195 46.963 49.645 28 12.461 13.565 15.38 16.928 18.939 37.916 41.337 44.461 48.278 5.993 29 13.121 14.256 16.47 17.78 19.768 39.87 42.557 45.722 49.588 52.336 3 13.787 14.953 16.791 18.493 2.599 4.256 43.773 46.979 5.892 53.672 4 2.77 22.164 24.433 26.59 29.51 51.85 55.758 59.342 63.691 66.766 5 27.991 29.77 32.357 34.764 37.689 63.167 67.55 71.42 76.154 79.49 6 35.534 37.485 4.482 43.188 46.459 74.397 79.82 83.298 88.379 91.952 7 43.275 45.442 48.758 51.739 55.329 85.527 9.531 95.23 1.425 14.215 8 51.172 53.54 57.153 6.391 64.278 96.578 11.879 16.629 112.329 116.321 9 59.196 61.754 65.647 69.126 73.291 17.565 113.145 118.136 124.116 128.299 1 67.328 7.65 74.222 77.929 82.358 118.498 124.342 129.561 135.87 14.169
F distribution critical value landmarks Table entries are critical values for F* with probably p in right tail of the distribution. Figure off distribution (like in Moore, 24, p. 656) here. De rees of freedom in numerator df1 2 3 4 5 6 7 8 12 24 1 39.86 49.5 53.59 55.83 57.24 58.2 58.91 59.44 6.71 62. 63.3 161.4 199.5 215.7 224.6 23.2 234. 236.8 238.9 243.9 249.1 254.2 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.6 976.7 997.3 117.8 452 4999 544 5624 5764 5859 5928 5981 617 6234 6363 45312 499725 54257 562668 576496 58633 593185 597954 61352 62373 63611 2 8.53 18.51 38.51 98.5 998.38 9. 19. 39. 99. 998.84 9.16 19.16 39.17 99.16 9.24 19.25 39.25 99.25 9.29 19.3 39.3 99.3 9.33 19.33 39.33 99.33 9.35 19.35 39.36 99.36 9.37 19.37 39.37 99.38 9.41 19.41 39.41 99.42 9.45 19.45 39.46 99.46 9.49 19.49 39.5 99.5 3 5.54 1.13 17.44 34.12 167.6 5.46 9.55 16.4 3.82 148.49 5.39 9.28 15.44 29.46 141.1 5.34 9.12 15.1 28.71 137.8 5.31 9.1 14.88 28.24 134.58 5.28 8.94 14.73 27.91 132.83 5.27 8.89 14.62 27.67 131.61 5.25 8.85 14.54 27.49 13.62 5.22 8.74 14.34 27.5 128.32 5.18 8.64 14.12 26.6 125.93 5.13 8.53 13.91 26.14 123.52.s ~ :!:!. c: e c: "C.5 E "C ~ ~ - m "' 4 5 6 4.54 7.71 12.22 21.2 74.13 4.6 6.61 1.1 16.26 47.18 3.78 5.99 8.81 13.75 35.51 4.32 6.94 1.65 18. 61.25 3.78 5.79 8.43 13.27 37.12 3.46 5.14 7.26 1.92 27. 4.19 6.59 9.98 16.69 56.17 3.62 5.41 7.76 12.6 33.2 3.29 4.76 6.6 9.78 23.71 4.11 6.39 9.6 15.98 53.43 3.52 5.19 7.39 11.39 31.8 3.18 4.53 6.23 9.15 21.92 4.5 6.26 9.36 15.52 51.72 3.45 5.5 7.15 1.97 29.75 3.11 4.39 5.99 8.75 2.8 4.1 6.16 9.2 15.21 5.52 3.4 4.95 6.98 1.67 28.83 3.5 4.28 5.82 8.47 2.3 3.98 6.9 9.7 14.98 49.65 3.37 4.88 6.85 1.46 28.17 3.1 4.21 5.7 8.26 19.46 3.95 6.4 8.98 14.8 49. 3.34 4.82 6.76 1.29 27.65 2.98 4.15 5.6 8.1 19.3 3.9 5.91 8.75 14.37 47.41 3.27 4.68 6.52 9.89 26.42 2.9 4. 5.37 7.72 17.99 3.83 5.77 8.51 13.93 45.77 3.19 4.53 6.28 9.47 25.13 2.82 3.84 5.12 7.31 16.9 3.76 5.63 8.26 13.47 44.9 3.11 4.37 6.2 9.3 23.82 2.72 3.67 4.86 6.89 15.77 7 3.59 5.59 8.7 12.25 29.25 3.26 4.74 6.54 9.55 21.69 3.7 4.35 5.89 8.45 18.77 2.96 4.12 5.52 7.85 17.2 2.88 3.97 5.29 7.46 16.21 2.83 3.87 5.12 7.19 15.52 2.78 3.79 4.99 6.99 15.2 2.75 3.73 4.9 6.84 14.63 2.67 3.57 4.67 6.47 13.71 2.58 3.41 4.41 6.7 12.73 2.47 3.23 4.15 5.66 11.72 8 3.46 5.32 7.57 11.26 25.41 3.11 4.46 6.6 8.65 18.49 2.92 4.7 5.42 7.59 15.83 2.81 3.84 5.5 7.1 14.39 2.73 3.69 4.82 6.63 13.48 2.67 3.58 4.65 6.37 12.86 2.62 3.5 4.53 6.18 12.4 2.59 3.44 4.43 6.3 12.5 2.5 3.28 4.2 5.67 11.19 2.4 3.12 3.95 5.28 1.3 2.3 2.93 3.68 4.87 9.36 9 3.36 5.12 7.21 1.56 22.86 3.1 4.26 5.71 8.2 16.39 2.81 3.86 5.8 6.99 13.9 2.69 3.63 4.72 6.42 12.56 2.61 3.48 4.48 6.6 11.71 2.55 3.37 4.32 5.8 11.13 2.51 3.29 4.2 5.61 1.7 2.47 3.23 4. 1 5.47 1.37 2.38 3.7 3.87 5.11 9.57 2.28 2.9 3.61 4.73 8.72 2.16 2.71 3.34 4.32 7.84 Critical values computed with Excel 9. F-table.xls 1 of2 12/24/25
Degrees of freedom in numerator (df1) p 1 2 3 4 5 6 7 8 12 24 1 1.1 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.28 2.18 2.6 4.96 4.1 3.71 3.48 3.33 3.22 3.14 3.7 2.91 2.74 2.54 6.94 5.46 4.83 4.47 4.24 4.7 3.95 3.85 3.62 3.37 3.9 1.4 7.56 6.55 5.99 5.64 5.39 5.2 5.6 4.71 4.33 3.92 21.4 14.9 12.55 11.28 1.48 9.93 9.52 9.2 8.45 7.64 6.78 12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.15 2.4 1.91 4.75 3.89 3.49 3.26 3.11 3. 2.91 2.85 2.69 2.51 2.3 6.55 5.1 4.47 4.12 3.89 3.73 3.61 3.51 3.28 3.2 2.73 9.33 6.93 5.95 5.41 5.6 4.82 4.64 4.5 4.16 3.78 3.37 18.64 12.97 1.8 9.63 8.89 8.38 8. 7.71 7. 6.25 5.44 14 3.1 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.5 1.94 1.8 4.6 3.74 3.34 3.11 2.96 2.85 2.76 2.7 2.53 2.35 2.14 6.3 4.86 4.24 3.89 3.66 3.5 3.38 3.29 3.5 2.79 2.5 8.86 6.51 5.56 5.4 4.69 4.46 4.28 4.14 3.8 3.43 3.2 17.14 11.78 9.73 8.62 7.92 7.44 7.8 6.8 6.13 5.41 4.62 16 3.5 2.67 2.46 2.33 2.24 2.18 2.13 2.9 1.99 1.87 1.72 4.49 3.63 3.24 3.1 2.85 2.74 2.66 2.59 2.42 2.24 2.2 6.12 4.69 4.8 3.73 3.5 3.34 3.22 3.12 2.89 2.63 2.32 8.53 6.23 5.29 4.77 4.44 4.2 4.3 3.89 3.55 3.18 2.76 a- 16.12 1.97 9.1 7.94 7.27 6.8 6.46 6.2 5.55 4.85 4.8 :!:!..B 18 3.1 2.62 2.42 2.29 2.2 2.13 2.8 2.4 1.93 1.81 1.66 c: 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.34 2.15 1.92.E 5.98 4.56 3.95 3.61 3.38 3.22 3.1 3.1 2.77 2.5 2.2 c: 8.29 6.1 5.9 4.58 4.25 4.1 3.84 3.71 3.37 3. 2.58, 15.38 1.39 8.49 7.46 6.81 6.35 6.2 5.76 5.13 4.45 3.69 = E 2 2.97 2.59 2.38 2.25 2.16 2.9 2.4 2. 1.89 1.77 1.61, 4.35 3.49 3.1 2.87 2.71 2.6 2.51 2.45 2.28 2.8 1.85 ~ 5.87 4.46 3.86 3.51 3.29 3.13 3.1 2.91 2.68 2.41 2.9. 8.1 5.85 4.94 4.43 4.1 3.87 3.7 3.56 3.23 2.86 2.43 "' 14.82 9.95 8.1 7.1 6.46 6.2 5.69 5.44 4.82 4.15 3.4 ~ Cl 3 2.88 2.49 2.28 2.14 2.5 1.98 1.93 1.88 1.77 1.64 1.46 c 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.9 1.89 1.63 5.57 4.18 3.59 3.25 3.3 2.87 2.75 2.65 2.41 2.14 1.8 7.56 5.39 4.51 4.2 3.7 3.47 3.3 3.17 2.84 2.47 2.2 13.29 8.77 7.5 6.12 5.53 5.12 4.82 4.58 4. 3.36 2.61 5 2.81 2.41 2.2 2.6 1.97 1.9 1.84 1.8 1.68 1.54 1.33 4.3 3.18 2.79 2.56 2.4 2.29 2.2 2.13 1.95 1.74 1.45 5.34 3.97 3.39 3.5 2.83 2.67 2.55 2.46 2.22 1.93 1.56 7.17 5.6 4.2 3.72 3.41 3.19 3.2 2.89 2.56 2.18 1.7 12.22 7.96 6.34 5.46 4.9 4.51 4.22 4. 3.44 2.82 2.5 1 2.76 2.36 2.14 2. 1.91 1.83 1.78 1.73 1.61 1.46 1.22 3.94 3.9 2.7 2.46 2.31 2.19 2.1 2.3 1.85 1.63 1.3 5.18 3.83 3.25 2.92 2.7 2.54 2.42 2.32 2.8 1.78 1.36 6.9 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.37 1.98 1.45 11.5 7.41 5.86 5.2 4.48 4.11 3.83 3.61 3.7 2.46 1.64 1 2.71 2.31 2.9 1.95 1.85 1.78 1.72 1.68 1.55 1.39 1.8 3.85 3. 2.61 2.38 2.22 2.11 2.2 1.95 1.76 1.53 1.11 5.4 3.7 3.13 2.8 2.58 2.42 2.3 2.2 1.96 1.65 1.13 6.66 4.63 3.8 3.34 3.4 2.82 2.66 2.53 2.2 1.81 1.16 1.89 6.96 5.46 4.65 4.14 3.78 3.51 3.3 2.77 2.16 1.22 Use StaTable, WinPep1 > Whatls, or other reliable software to determ1ne spec1ficp values F-table.xls 2 of2 12/24/25