ESSAYS ESSAY B ESSAY A and 2009 are given below:

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1 ESSAYS Suggested time: 5 minutes Maximum score: 120 points ESSAY A Suggested time: 5 minutes Maximum score: 120 points I. Define a time series and its components. Discuss the importance and the use of time series in business and economics. ESSAY B The job of a statistician is not yet completely done once the data have been collected, processed and professionally edited and compiled. Statisticians also need to be concerned that their final product reaches the designated audiences and is being used appropriately and effectively. This final stage of the data-management process is referred to as "data dissemination". II. In a certain industry, the production of a commodity (in t000 units) during the year 1999 and 2009 are given below: a) What are the various modes by which data can be disseminated, in other words, in what form can statistical data be transmitted from the statistical producer to the users? Discuss Year Production ('000 units) briefly the advantages and disadvantages of the various current modes of data dissemination? b) Data dissemination by a national statistical office in many countries is governed by a comprehensive dissemination policy. Which are the elements that need to be addressed in such a dissemination policy? c) To what extent should a statistical agency perform and disseminate analysis and forecasting? d) Some experts propose to move from the term ÿ'data dissemination" to "data communication". Please explain why? a) Graph the data b) Obtain the least square line fitting the data and construct the graph of the trend line Begin writing your answer to Essay B on page 21 of the answer booklet. c) Interpret (explain) the estimated parameters. d) Compute the trend values for the years and estimate the production of the commodity during 2010 and 2011 if the present trend continues. e) Eliminate the trend assuming additive and multiplicative models. Begin writing your answer to Essay A on page 15 of the answer booklet.

2 -9- QUESTIONS QUESTION 1 The number of individuals in the population Pt is 100,000. QUESTION 3 If X is the amount of money (in dollars) that a salesperson spends on gasoline and Y is the corresponding amount of money for which he/she is reimbursed, the joint density of these two random variables is given by: (b) Suppose this population is growing geometrically at an annual rate r = If r is compounded annually- i.e., the population PI at the end of 1 year equals P0(l+r), determine the size of the population at the end of 10 years. If the population is growing arithmetically with an increment of 0.02 of its initial number per year, what will be the size of the population at the end of 10 years? --<Y<X 25\ X ) 2.( O- "ÿÿz_ 2ÿ_X for 10<X<20, X f(x,y) =, O, elsewhere (c) Calculate the difference between the population size calculated with assumption (a) and with assumption (b) at the end of 100 years. Begin writing your answer to question 1 on page 33 of the answer booklet. Find: a) b) c) the marginal density of X the conditional density of Y given X=15 the probability that the salesperson will be reimbursed at least $10 when spending $15. Begin writing your answer to question 3 on page 1 of the answer booklet. QUESTION 2 In a dice game, getting: a) two pairs b) four of a kind c) five balanced dice are rolled a full house (three of a kind and a pair) simultaneously. Find the probability of Begin writing your answer to question 2 on page 37 of the answer booklet. QUESTION A sample of 30 students is to be drawn from a population consisting of 300 students belonging to two colleges A and B. Means and standard deviations of their marks are given below: Total number of students (N,) Mean XNÿ College A College B Standard deviation O-i 10 0

3 a) Draw a sample using proportional allocation. b) Obtain the variance of the estimated population mean. c) Based on the results in b), compare the efficiency of the stratified sampling with simple random sampling without replacement. Begin writing your answer to question on page 5 of the answer booklet. QUESTION Since the late 1980s, improving maternal health and reducing maternal mortality have been the key concerns of several international summits and conferences. QUESTION 5 In the last two decades there have been great advances in the use of Geographic a) Provide the formula and describe the basic measures of Maternal Mortality (Maternal Mortality Ratio and Maternal Mortality Rate). b) Describe the data sources (and their related major issues) for measuring accurately the levels of maternal mortality in a population. Information Systems (GIS) in statistics. Describe how GIS and other geospatial tools (GPS, Satellite imagery, etc.) can be applied in the phases of census (census preparation, data collection, data processing and data dissemination). Elaborate the advantages of applying GIS Begin writing your answer to question 7 on page 57 of the answer booklet. in these processes? Begin writing your answer to question 5 on page 9 of the answer booklet. QUESTION 8 QUESTION 6 Before an increase in the excise duty on tea, 800ÿpersons out of a sample of 1,000 persons were found to be tea drinkers. After an increase in duty, 800 people were tea drinkers in a sample of 1,200 people. Two shipment lots of manufactured items are randomly sampled to determine whether the proportion of defective items is different in the two lots. The table contains the result of a survey of 125 items. Shipment lot\ Findings A B Total Defectives Non-defectives Total a) b) Using standard error of proportions, state whether there is a significant decrease in the consumption of tea after the increase in excise duty, at 5 per cent of significance. Furthermore, calculate the 95% confidence interval of the proportion of tea drinkers in the whole population after the excise duty has been increased. I Based on the above information from the survey, test the hypothesis that there is no significant difference between the proportion of defective items of shipment lot A and B in the whole shipment at 5 per cent of significance. Begin writing your answer to question 6 on page 53 of the answer booklet. Begin writing your answer to question 8 on page 61 of the answer booklet.

4 -13- QUESTION 9 The following table shows quantities and prices per unit of two commodities measured over three years. Both commodities are representatives of the same industry. Commodity A Commodity B Year Quantity Price, $ Quantity Price, $ a) b) c) Calculate the Laspeyres volume indices for this industry for years 2001 and 2002 for fixed base year Calculate the Laspeyres volume index for this industry as an almually chained index for the reference year Compare and enumerate advantages and disadvantages of fixed base index versus chain index. Begin writing your answer to question 9 on page 65 of the answer booklet.

5 page 31 page 32 Annex/Annexe Standard normal distribution areas The t-distribution / Mean z z 0.t z : , t, , O.7 _258O ' t2! : , : ÿ !06.3i ' ,706 3! , , t 82, , ):.015.2, "ÿd32 6 1, , ÿ07 7 1, "365 2,998 3, , ,372 "t.812 2, :ÿ ÿ : f , " , , ! _106 3.o ÿ t20 2, ÿ ,ÿ ÿ ÿ , , ,861 2, , , , ÿ ] : t ! , , , ,323" " !.321 ' , _ , , , , , , ÿ) ÿ O ÿ _ oo 1, ,ÿ23 2, :

6 The x2-distribution page 33 page 3 (concluded) / O O0O ".00,010 ".020 [051 " " ; t t '.9 1" :82, ; ' ' : , , "1.0 12: ll.5 13:1 1:6.ot ,31".10.1 t0.9 11: t O B ' , O O O : 16.2 t0. " () / t5.0 16,8 18, , , : fl ! _ t _ O O O / t ' ,

7 The FZdistribution page 35 (continued) page 36 ' ÿ I ÿ , , : o _ _999 I" I I '!.89 t [ t " ,052 5,000 5,03 5,625 5, ,928 5,981 6,022 16,211 20,000 21,6t5 ÿ2, ,37 23ÿ,7! 5 23,925 2,091 05, ,000 50, ,500 "576, ,ÿ.70 -_598,10 602, I.I 3 1,2! : I '6 9: t l-9. I : , " : ÿ8I I.I, " : ÿ l " " 3. I 30.8 " ' , :-5.8. ". 1 3,9 "167_ "1.t , , ,32,19.11,05 _ ;9 7.7 t , _ 16 6, , " I6, , " 21." , I ÿ ;5 0,528 0, ,965 t I D ,37 3, ,79 5,I 5,19 3, " 7,76 7_39 " t, ÿ 10, "22.8" 18ÿ3 16.5!5, _ , " 28,8 " "80 0, '00 1: , " " 3; " I-.28.,21. t :7" I "lo.g t " " t , " : " " " " " I 9 " " I d t t_6 1.3 I-= 1 -- ÿ to m O ",95 5 9, ,056 2,22 605, ' 985 6,106-6,157 2,26 2, , , t.36 9, t , ' _ , , ÿ3 " I I'.05 1,06 1: _06 "_00 3ÿ " I 8_0. I 7.6 {.03 1, : )[ I' [ l # ' ,001 1,010 1,01 1,018 6,209 6,235 6,261 6,)13 6,339 6,366 2, , ,359 25,6 620,910 62S, , ,30 633, , ,t ,3 1. 9ÿ _7 9.8 "9.9 " t9.5 39, , , , 99, _ I , I _ t , t,1! " I 2.8 2, ,1 t.15" 1.16 I.t _ , / _ t 8ÿ6 8, I , ' I 5,8 3., , ' ,8 12_0! 23.5 " [ 8_9_ " t t,ll , t_ l " ' ,0,37 6" I t ÿ1 25: 25. I ! !.10 1, , _81-3", t _ ,97 6.' ,12 9, ' t I _ ÿ !

8 The F-d'istributio n page 37 page 38 (c o ntin ued) 1"I 1"1 r= 1 -- ÿ 10 t m r _ , l _ , I I I 2.73 ÿ ' " , f '12.0 I " " '2: , ",32 ÿ20. I , I t.7 / 1.1 I '., : ! ,05 t"106 1,07.I ,38 2_3. 3, , ,08 " , , " :03 7, " 6,61 6, , f" 9, , , , ÿ77 5,26 5. t I ,23 6, t.05, t , ,65, : _29 2_ " , :ÿ I0..9"9,5,9!2, , , , I _ I ,ÿ , ! 6 2.1' t _ " 5, " I ÿ , : "8 ' " _25 2. t " 2.0 " ' _ " { , _ : " G , ' , " ".93 0, , _ I2 " :95" 5.1 5, ' , ,09 '2.59 " ' 1" " " 0ÿ , ÿ , :90 3ÿ67 " 3 3_ , : ÿ I , I ' ".2,15 2, _ : " , , , i.88 2_ , '.39 t t ,09 3, '.1 I ,37.I , , ,29 2 : ,00 1, , , t _ " 7.7 2; t , ! ! t 2.6" t2 'l: " , , ,02 1,61 "t.8 2; I, , , i , ' , , i ! : " t ,26,

9 page 39 page -0 The F-distribution (con Hnued) rl (concluded) r2 I--cÿ l"t 30.5O " 5,999 60,50 ' ,995 9 m. 5, : " 1, , " 5.57 " " _57" i , , /t "6.12 5, I 0, I , , _00 3, , , ,3 3.01" " 2,51" 2.t" ,95 2, ,7.3 " " , ÿ , _8 0.8T I ' ÿ ,95, , ,789 0, ,9t8 0, t ÿ{ t.67 t , [,88 5_ '.19 2_ '2.62 " , t0!' cÿ! t 20 :ÿ 30 6O 120.co 5 9, ' I, t ! :92 t I.9 1, , " 2, : , , , , :999 : , I ÿ !, ! "I !,8 t ÿ '2,l 2_3I " 1_87 1, ÿ2t -2.! I I 8 3.0t 2_ : , ' _32" 1.26 I "t !.66 t ,3 1_ f ' I 2:7 " t.86 t, I _ " 1.61 t , , " 0,95 0, , t.55 1: t , ,.6!.32 2, ÿt, t ÿ) ; , , I t I.00 t o