namibia UniVERSITY OF SCIEnCE AnD TECHnOLOGY FACULTY OF HEALTH AND APPLIED SCIENCES DEPARTMENT OF MATHEMATICS AND STATISTICS MARKS: 100

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1 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

2 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 Frequency 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 y 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

3 Marital status Gender Male Female Total Single Married Divorced Widowed Total 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) Xl X X (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 = and that MSE = [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

4 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 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] 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

5 t-distribution Table /\ ~ t The shaded area is equal to a fort= ta.!.too t.oso t.25 t.oto t.oos Gillcs Cazclais. Typeset with k\tex on Apri12, 26.

6 Chi-Square Distribution Table The shaded area is equal to ex for x 2 = x;. df X~ggs X 2 ggo X X~gso X 2 goo X~wo X 2 oso X 2 o2s X~o1 x:oos

7 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 df s ~ :!:!. c: e c: "C.5 E "C ~ ~ - m "' Critical values computed with Excel 9. F-table.xls 1 of2 12/24/25

8 Degrees of freedom in numerator (df1) p a :!:!..B c: E c: , = E , ~ "' ~ Cl c Use StaTable, WinPep1 > Whatls, or other reliable software to determ1ne spec1ficp values F-table.xls 2 of2 12/24/25