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II Index No:LINWERSITI SAINS MALAYSIAPeperiksaan Kursus Semasa Cuti panjangAcademic Session 2008/2009Jun 2009JKE 316E - Quantitative EconomicsfEkonomi KuantitaffiDuration: 3 hoursfMasa : 3 jamJINSTRUCTIONS TO CANDIDATES' This examination paper consists of NINETEEN pages, Appendix A (formula) andAppendix B (Table Z,tandF).o Answer ALL questions. You may answer either in Batrasa Malaysia or in English.o Write your answer in the space provided only.ARAHANSila pastikan bahawa lcertas peperilcsaan ini mengandungi SEMBILAN BELAS mutrasurat yang bercetak, Lampiran A (Formula) dan Lampiran B (Jadual Z, t dan F), sebelumanda memulakan p ep eriks aan.Jawab SEMUA soalan. Anda dibenarkan menjawab soalan sama ada dalam BahasaMalaysia atau Bahasa Inggeris.Tulis jawapan anda di ruangan yang disediakan.Angka Giliran:Pusat Peperiksaan:Tarikh Peperiksaan:24',7...21-248Index No:1. Write short notes on:(Tulis nota ringkas tentang:)(a) Type I error(Ralat jenis I)(b) Type II error(Ralat jenis II)(c) Interval data(Data interval)-2- IJKE 31681(3 marks)(3 markah)(3 marks)(3 markah)(3 marks)(3 markah)al...J/-24sIndex No: IJKE 316E](8 marks)(8 markah)(8 marks)(8 markah)-3-(d) Measures of central location(P engulatr an I okas i memus at)(e) Cluster sampling(Persampelan kluster)...4t-250Index No: IJKE 316E1(3 marks)(3 markah)(3 marks)(3 markah)(3 marks)(3 markah)4-You are given with the following information.(Anda diberi maklumat berilrut)Ho: p: 1,000Ha: p I 1,000x : 980, n: 100, and o =200. o,:.01(a) Find the value of test statistic(Cart nilai ujian statistik)(b) Interpret the result(Beri tafsiran keputusan yang anda perolehi di, atas)(c) Draw the sampling distribution(Lukis taburan p ers amp elan)251...5/-Index No:)-(d) Explain the importance of hypothesis testing(Jelaskan kepentingan uj ian hipotesis)(e) Describe the process of conducting a hypotheses testing(Jelaskan pro s es menj alankan uj ian hip otes is)IJKE 316E1(3 marks)(3 markah)(8 marks)(8 markah)252...6t-Index No: UKE 316E1-6-(0 A traffic police officer claimed that the average speed of cars exceeds the limitof 110 kilometer per hour. The speeds of a random sample of 100 caxs wererecorded at 115 kph. Assume the standard deviation is 8 kph, determine whetherthe claim by the officer can be substantiated. Use 5% significant level.(10 marks)(Seorang pegawai polis mendala,va bahawa purata kelajuan kereta adalahmelebihi 110 km sejam. Kelajuan satu sampel rawak 100 kereta ialah II5 kmseiam. Andaikan sisihan piawai ialah 8 kilometer sejam, tentukan sama adadah,vaan pegawai itu dapat diterima. Guna 50% paras Leertian.)(10 markah)253. ..7 t-Index No: IJKE 316E]-7 -...8/-254Index No:-8-3. (a) Complete the following ANOVA tableshaded cells onlv.(Lengkapkan jadual ANOI/A di bawahp etak y ang dikelabukan)UKE 316E1by writing the correct figures in the(12 marks)dengan menulis angka yang betul di(12 markah)(b) The sample size (n) for the study was(Saiz sampel (n) kajian ialah _.)(c) Test to determine whether the treatment means differ. (use o : .05)(Uji sama ada min ujikaji berbeza. Guna a : .05)(2 marks)(2 markah)(3 marks)(3 markah)255...9t-Index No: IJKE 316E1(3 marks)(3 markah)9-(d) Test to determine whether the block means differ. (Use o : .05)(Uji sama ada rnin blok adalah berbeza. Guna a: .05)256...t0/-lndex No:-10- FKE 316E1(2 marks)(2 markah)4. The relationship between years of experience and amount of sales closed bv sixrandomly selected salesmen is shown in the folrowing table. n:6.(Hubungan antara pengalaman dan jumlah jualan yang dibuat oleh enam jurujualyang dipilih secara rawak adalah seperti di dalam jadual. n : 6)(a) Plot a scatter diagram for the above data.(Buat rajah sebaran untuk data di atas)5617 1212346195Experience, X (years)25',7...rlt-Lrdex No: IJKE 316E1- 11-(b) Calculate the least squares line and interpret the coefficients. Use the followinginformation in your calculation:(8 marks)(Dapatknn garis lansa dua terkecil dan beri tafsiran koefisien. Guna maklumatberilrut dalam pengiraan anda)(8 markah)X xy: 37.76 Ex2 : 42.79S*r:7.4 52*: 3.5258...r2/-Index No: UKE 316E1(8 marks)(8 markah)(c) (i)-12-List and explain the time series components(Senarai dan jelaskan komponen siri masa)259...t3/-Index No: IJKE 316E]_13_(ii) Describe the smoothing techniques used to reduce random variation intime series data.(7 marks)(Huraiknn kaelqh smoothing yang digunakan untuk mengurangkanvariasi rawak dalam data siri masa.)(7 markah)260...t41-Matric No:Test statistic for p.Test statistic Z =Test statistic t =Sample slope)_,,. 4=a5;Sample 7-interceptbs=y-briSum ofsquares for errornsSE: 2U,- y),Standard error of estimateTest statistic for rhe slope. br- Ftr:-5b,Standard error of &,' Y(" - t)'1-t4-F'ORMULASCoefficient of determinationIJKE 316E]APPENDIX A2(v,- n'V-polJ;X-pSl'!n)-JnR':-;j; =l--a -z-x-y,Prediction intervalI t l* -i\2)' ! to,r,n-rs,^lt +: + )^s i/^n (n - t)rjConfidence interval estimator of the expected value of ylt (- - -)zi t top,n-zs4l:+ H;(n - I)s'z,1)siSample coefficient of correlation-ryf--J.J.,fTest statistic fbr testing p : 0261...1,s1-Matric No:I Least Squares Line CoefEcients,Sryul - .bo: V - briwhereIJKE 316E],r6t-262-15-ttsl\)r.ZJ *lftns) 1r.ZJ 'tri:lV:-'flMatric No:-16-FORMULASOne-way analysis of variancekSST = )"1G1-V)'j: tknie(F=SS('..-n.\2Z.r ./-r \*U '1/j=r i=LMSr: illk- |SSEMSE: - ,n- KMSTt--'-MSETwo-way analysis of variance (randomized block design ofexperiment)kbSS(Total) j=t ;=tkssr: )u1z;r1,_=*1,i= IbSSB: >/c(tlBlr-t)'?t= IkbSSE : j=t i=rMST:*MSB : SSBb-rSSEMSE: k-b+1IJKE 316E]Two-factor experimentabrSS(Total)i=l i:l k:lSS(A) : rb)('lAl.-=x)'1oss(B) : ra)6ln)'-:x1';: Iss(AB) : ,2 ittt*lu - t[A], - t[B]i + t)'?i=l j=tabrSSE :t=l j=l k=lSS(A)MS(A) a- ISS(B)MS(B) : :--b-lMS(AB) =ss(AB)(a-r)(b-r)n-MSTE--'-MSEMSBD--'-MSEMS(A)tr- -'L_ MSEMS(B)E - ---------'- MSE_ ' MS(AB)ts:-^ MSELeast significant difference comparison methodTukey's multiple comparison method. &sEo : 4o(K, r)tl \263...17 t-Matric No:Table 3 Normal Probabilities-17 -IJKE 316E]APPENDIX B.0040.0438.0832.1217.1591.1950.229"t.2611.291,0.3186.3438.3665.3869.4049.4207.4345.4J.63.4564.4649.4779.4778.4826.4864.4896.4920.4940.495s.4966.4975.4982.4987.0080.0478.0871,.1255.1628.1985.2324.2642.2939.32t2.346r.3686.3888.4066.4222.4357.474.4573.4656,4726.4783.4830.4868.4898.4972.4941,.4956.4967.4976.4982.4987.0279.0675.1064.1M3.1808.2157.2486.2794.3078.3340.JJ/ /.3790.3980.4147.4292.441.8.4s;5.461.6.4693,+t30.4808.4850.4884.4911.4932.4949.4962.4972.4979.4985.4989.0120 .0160.0517 .0557.0910 .0948.1293 .1331.1664 ,. t.t700.2019 .2054.2357 .2389.2673 .2704..2967 .2gg5.3238 ,3264.3485 .3508..3708 .3729.3907 .3925.4082 .4099.4236 .4251.4370 .4382.4484 .4495.4582 .4591.4564 .4671..4732 .4738.4788 .4793.4834 .4838.4871, .4875.4901. .4904.4925 .4927.4943 .4945.4957 .4959.4968 .4969.4977 .4977.4983 .4984.4988 .4988.0199 .0239.0596 .0636.0987 .7026.1368 .1,406.1736 .1n2.2088 .21,23.2422 .2454.2734 .2764.3023 .3051.3289 .3315.3531 .3554.3749 .3770.39M .3962.411,5 .4131.4265 .a79.4394 .M06.4505 .4515.4599 .4608.4678 .4686.47M .4750.4798 .4803.4842 .4846.4878 .4881.4906 .4909.4929 .493.t.4946 .4948.4960 .4967.4970 .4971.4978 .4979.4984 .4985.4989 .4989/fu0z0.0 | .00000.1 | .0398q.2 | .07e30.3 | .17790.4 | .15540.5 | .19150.6 | .22s70.7 | .25800.8 | .288i0.9 | .31591.0 | S+rs1.r I '3643L.2 | .3849r.3 | .40321.4 | .41921.5 I .43321..6 | .M52r.7 | .4554L.8 | .4U1,r.9 | .47132.0 | .4n22.'t | .482L2.2 | .48612.3 | .48e32.4 | .49182.5 | .sgse2.6 | ,49532.7 | .49652.8 | .49742.9 | .sgst3.0 | .+gezsouRcE: Abridged from Tabre i of A. Hald, statistical Tables and Formulas (New york: wiley & sons, Inc,), 1952. Reprod.uced bypermission of A. Hald and the publisher, John wiley & sons, Inc. ^"..'' ""-./ s rurr! urr'/ ,..1g/_.0319 .0359.071,4 .0753.1103 .1141.1480 .1517.7844 ,1879.2190 .2224.2517 .2549.2823 .2852.3106 .3133.3365 ,3389.3599 .362.1.3810 ,3830.3997 ,4015.41.62 .41n.4306 .4319.M29 .441..4535 .4545.4525 .4633.4699 .4706.4761 .4767.4812 .4817.4854 .4857.4887 .4890.491.3 .491.6.4934 .4936.495"t .4952.4963 .4964.4973 .4974.4980 .4981.4986 .4985.4990 .499A264Matric No:Table 4 Critical Values of f-18-IJKE 316E]DEGREES OFFREEDOM f,.rco f.oso t.ors f.oro f.oosDEGREES OFFREEDOM ,-100 f.orot.ozsr.050 f,.oosI23456891011t213t4t5"t6'171819202122233.078 6.3141.886 2.920i.638 2.3531.533 2.7321..476 2.0151*M0 1..9431.415 i.8957.397 1.8501..383 1.8337.372 1..8721.363 1..7961,.356 1.7821.350 1,.77r1.345 1.7671.341 1.7537.337 1.7461.333 t.7401.330 L.7Ur.328 1.7291.325 1.7251.323 r.7271.321 'L7171.319 1.71.412.706 3i.8214.303 6.9653.182 4.5472.776 3.7472.577 3.3652.447 3.1.432.365 2.9982346 2.8962.262 2.8212.228 2.7642.20t 2.71,82.179 2.6812.t60 2.5502.745 2.6242.13L 2.6022.120 2.5832.110 2.5672.101, 2.5522.093 2.5392.086 2.5282.080 2.5182.074 2.5082.069 2.50063.6579.9255.8414.6044.0323.7073.4993.3553.2503.1693.1063.0553.0722.9n2.9472.9212.8982.8782.8512.U52.8312.8192.80724z326272829303540455060708090100't20ua160180200&1.318 7.711.7.376 1..7081.315 1..7061.3"14 1..7031.313 7.701.1.311 1.6991.310 1..6971.306 1..6901.303 1.5841.301 1..6791.299 1.6761..296 1..671.1,.294 . 1.6671..292 1,.6641.241 1.6621..290 1..6601,.289 1.6581.288 1.6561..287 1,.6541..286 1.6531,.286 1.6531..282 1.6452.064 2.492 2.7972.050 2.485 2.7872.056 2.479 2.7792.052 2.473 2.7712.048 2.467 2.7632.045 2.462 2.7562.042 2.457 2.7502.030 2.438 2.7242.021, 2.423 2.7052.014 2.412 2.6902.009 2.403 2,6782.000 2.390 2.5601.994 2.381 2.6481.990 2.374 2.639L987___2369____2,6n1.984 2.364 2.6261.980 2.358 2.6171,9n 2353 2.611,1.975 2.350 2.607't.973 2.U7 2.6031.972 2.345 2.601,1,.960 2.326 2.576souRcE: From M. MerringtorL'Table of Percentage Points of the f-Dishibu &on" Biometrika32 (194i):300. Reproducedby permissionof the Biometrika Trustees.265...r9t-Matric No:Table 6[a) Critical Values of F: A = '051 | 761.4 199.518.51 19.003 I 10.13 9.556.945./95.145.59 . 4.74-19-NUMERATOR DEGREES OF FREEDOMIJKE 316E]236.8 238.919.35 19.37456,7891011't2Bi3n14E1s6tefrt/618o 1q920z 2'I5^^OALz^^EZJ2425262728293040601?n7.71.6.615.995.325.124.964.844.754.674.604.544.494.454.4't4.384.J54.324.304.284.264.244.234.21.4.204.78t 1n4.084.003.92J.644.464.264.103.983.893.813.743.683.533.593.555.523.493.473.43.423.403.393.373.35J.J1T3.323.233.153.473.008.896.094.884.213.793.503.29c1L3.012.912.832.752.7"12.662.6L2.582.542.512.492.462.M2.422.402.39z,J/2.362.35/.,3J2.252.172.092.018,856.044.824.15J./C3.4J.ZJ3.072.952.852.n2.702.642.592.552.512.482.452.422.40z.J/2.362.342.322.31.2.292.282.272.182;t02.021,.9424U.319.388.816.004.774.103.683.393.183.022.902.802.712.652.592.542.492.452.422.392.372.342.322.302.282.272.252.242.222.21.z, rz2.041..961.88215.7 224.6 230.2 234.019.1,6 19.25 19.30 19.339.28 9:12 9.01 8.946.59 539 6.26. 6.1.65.41 5.19 5.05 4954.76 4.53 4.39 4.284.35 4.72 3.97 3.874.07 3.W 3.69 3.583.86 3.63 3.48 3.373.71, 3.48 3.33 3.223.59 336 3.20 3.093.49 3.26 3.11 3.003.4't 3.18 3.03 2.92334 3.11 2.96 2.853.29 3.06 2.90 2.793.24 3.01 2.85 2.743.20 2.96 2.8L 2.703.16 2.93 2.77 2.663.13 2.90 2.74 2.633.10 2.87 2.71 ,. 2.603.07 2.84 2.68 2.573.05 2.82 2.66 2.553.03 2.80 2.64 2.533.01 2.78 2.62 2.5't2.gg 2.76 2.60 2.492.98 2j4 2.59 2.472.96 2.73 2.57 2.462.95 2.71. 2.56 2.452.93 2.70 2.55 2.432.92 2.69 2s3 2.422.84 2.61 2.45 2.342J6 2.53 2.37 2.252.68 2.45 2.29 2.172.60 2.37 2.21, 2.1.0souRcE: From M. Merrington and C. M. Thompson, "Tables of Percentage Points of the Inverted Beta (F)-Distribution," Biometrika33 (1943): 73-88. Reproduced by permission of the Biometrika Trustees.-ooo000ooo-266

JKE316E - QUANTITATIVE ECONOMICS JUN 2009

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JKE316E - QUANTITATIVE ECONOMICS JUN 2009

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