APPLIED STATISTICS Complementary Course of BSc Mathematics - IV Semester CUCBCSS Admn onwards Question Bank

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Hugo Randall
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1 Prepared by: Prof (Dr) K.X. Joseph Multiple Choice Questios 1. Statistical populatio may cosists of (a) a ifiite umber of items (b) a fiite umber of items (c) either of (a) or (b) Module - I (d) oe of (a) ad (b) 2. W hich of the followig ca classified as a hypothetical populatio (a) All labourers of a factory (b) Female productio of a coutry (c) Populatio of real umbers betwee 0 ad 100. (d) Studets of the world 3. A study based o complete eumeratio is kow as (a) sample survey (c) cesus survey (b) pilot survey 4. Method of complete eumeratio is applicable for (a) kowig the productio (b) kowig the quatum of export ad import (c) kowig the populatio 5. First step i a statistical equiry is (a) plaig the equiry (c) forecastig 6. Samplig frame refers to (a) the umber of items i the sample (b) collectio of data (d) orgaisatio (b) the umber of items i the populatio (c) listig of all items i the populatio (d) listig of all items i the sample. 7. A sample cosists of (a) all uits of the populatio (b) 50% of uits of the populatio (c) 5% of uits of the populatio (d) ay fractio of the populatio 8. Samplig is ievitable i the situatio (a) blood test of a perso (b) whe the populatio is ifiite (c) testig of life of battery cells 9. W hich of the followig represets data. (a) A sigle value (b) Oly two values i a set APPLIED STATISTICS Complemetary Course of BSc Mathematics - IV Semester CUCBCSS Adm owards Questio Bak

2 (c) A group of values i a set (d) Noe of the above 10. Startified radom samplig is used whe (a) populatio is heterogeeous w.r.t some characteristics (b) Whe populatio is homogeeous (c) W he populatio is fiite 1 1. Statistical data are collected for (a) Collectig data without ay purpose (b) a give purpose 1 2. Eumerators are persos (c) ay purpose (a) who coducts the ivestigatio (b) who gathers the iformatio from iformats (c) who gives the iformatio 1 3. Simple radom sample ca be draw with the help of (a) radom umber tables (c) roulette wheel (b) chit method 1 4. If the items are destroyed uder ivestigatio, we have to go for (a) complete eumeratio (c) both (a) ad (b) (b) samplig studies (d) either (a) or (b) 1 5. Selected uits of a systematic sample are (a) ot easily locatable (b) easily locatable (c) ot represetig the whole populatio 1 6. Radom samplig is also termed as (a) probability samplig (c) both (a) ad (b) (b) chace samplig 1 7. W hich of followig is a type of probability samplig (a) W here each uit has equal chace of beig selected. (b) Samplig uits have differet probabilities of beig (c) Probability of selectio of a uit is proportioal to (d) All the above 1 8. W hich of the followig is a mixed samplig method. (a) Stratified radom samplig (b) Systematic samplig (c) Cluster samplig (d) All the above 1 9. Cluster samplig is a method of (a) Radom samplig (c) Ay samplig (b) o radom samplig selected the sample size 2 0. I srs with replacemet, the probability of selectig a specified uit of the populatio at ay draw has (a) A uequal chace (c) Chace is proportioal (b) Equal chace 21. The probability of a uit to be icluded i a sample of size take from the populatio of size N is (a) 1 N (b) 1 c) N d) 1 NC

3 2 2. Ay value computed usig populatio observatios is called (a) statistic (b) parameter (c) estimator 2 3. The differece betwee statistic ad parameter is called (a) No samplig error (b) stadard error (c) Samplig error is devoid of samplig errors (a) Samplig survey (c) Questioaire method (b) Cesus survey 2 5. Samplig error ca be reduced to a larger extet by (a) decreasig sample size (c) icreasig sample size 2 6. Questioaires ad schedule are (a) Same i its kid ad degree (b) Costat sample size (b) Same i its degree ad vary i its kid (c) Vary i its kid ad degree (d) Same i its kid ad vary i its degree. ANSWERS 1. c 2. c 3. c 4. c 5. a 6. c 7. d 8. d 9. c 1 0. a 1 1. b 1 2. b 1 3. d 1 4. b 1 5. b 1 6. c 1 7. d 1 8. d 1 9. a 2 0. b 2 1. c 2 2. b 2 3. c 2 4. b 2 5. c 2 6. d Multiple Choice Questios Module - II 1. The idea of testig of hypothesis was first set forth by (a) R.A. Fisher (c) E.L. Lehma (b) J. Neyma (d) A. Wald 2. Equality of two populatio variaces ca be tested by (a) t- test (c) both (a) ad (b) (b) F-test (d) either (a) or (b) 3. Equality of several ormal populatio meas ca be tested by (a) Bartlett s test (b) F-test (c) 2 test (d) t-test 4. The ratio of betwee sample variace ad with i sample variace follows (a) F-distributio (b) 2 distributio (c) Z-distributio d) t- dis tributio 5. Aalysis of variace utilizes (a) F-test (b) 2 test (c) Z-test (d) t- test 6. Customarily the large variace i the variace ratio for F statistic is take (a) i the umerator (b) i the deomiator (c) eitherway

4 7. The variace due to two treatmets i a experimet is 480 ad the error variace is 60.0 with 14 df. Test for equality of treatmet effects reveals that (Give F [0.05, (1, 14)] = 4.60) (a) treatmets are equally effective (b) treatmets differ sigificatly (c) o coclusio 8. The error degrees of freedom for two-way ANOVA with r rows ad c colums is (a) r 1 (b) c 1 (c) (r 1) (c 1) (d) rc 1 9. The aalysis of variace techique is based o the assumptio (a) Populatios from which the samples have bee draw are ormal. (b) The populatios have the same variace (c) The radom errors are ormally distributed (d) All the above 10. The techique of Aalysis of variace was first devised by (a) Karl Pearso (c) Irwig Fisher (b) R.A. Fisher (d) W.Z. Gosset ANSWERS 1. b 2. b 3. b 4. a 5. a 6. a 7. b 8. c 9. d 1 0. b 2 9. F=5.43, Reject 3 0. F=16.3, Reject 3 1. F=1.57, Accept 3 2. F=3.85, Differet 33. (a) F=1.01, No (b) F=3.29. Module - III Multiple Choice Questios 1. Idex umber is a: a) measure of relative chages b) a special type of a average c) a percetage relative d) all the above 2. Idex umbers are expressed: a) i percetages b) i ratios c) i terms of absolute value d) all the above 3. Idex umbers help: a) i framig of ecoomic policies b) i assessig the purchasig power of moey c) for adjustig atioal icome d) all the above 4. Idex umbers are also kow as: a) ecoomic barometers b) sigs ad guide posts c) both (a) ad (b) d) either (a) or (b) 5. Most commoly used idex umber is: a) Diffusio idex umber b) price idex umber c) value idex umber d) oe of the above

5 6. Oe of the limitatios i the costructio of idex umbers is: a) the choice of the type of average b) choice of ivestigators c) choice of variables to be studied d) all the above 7. The first ad fore most step i the costructio of idex umbers is: a) choice of base period b) choice of weights c) to delieate the purpose of idex umbers d) all the above 8. Base period for a idex umber should be: (a) a year oly b) a ormal period c) a period at distat past d) oe of the above 9. The uweighted price idex formula based o items is: a) p 1 / p 0 b) p p c) p p d) oe of the above 10. Laspeyre s idex formula uses the weight of the: a) base year b) curret year c) average of the weights of a umber of years d) oe of the above 11. Laspeyre s idex umbers possess: a) dowward bias b) o bias c) upward bias d) oe of the above 12. The weights used i Paasche s formula belog to: a) the base period b) the give period c) to ay arbitrary chose period d) oe of the above 13. Paasche s quatity idex formula for items is: a) p q p q b) p q p q 1 1 / / c) p q / p q 100 d) p q p q / The Drobish-Bowley price idex formula is the: a) geometric mea of Laspeyre s ad Paasche s price idex b) arithmetic mea of Laspeyre s ad Paasche s price idex c) Weighted mea of Laspeyre s ad Paasche s price idex d) oe of the above 15. The price idex as the arithmetic mea of Laspeyre s ad Paasche s idices was expouded by: a) Kelly b) Irvig Fisher c) Drobish ad Bowley d) Walsh

6 16. The geometric mea of Laspeyre s ad Paasche s price idices is also kow as: a) Fisher s price idex b) Kelly s price idex c) Drobish-Bowley price idex d) Walsh price idex 17. Marshall ad Edgeworth price idex umber formula utilises the weights as: a) quatities of the base year b) quatities of the give year c) combied quatities of base ad give year d) ay of the above 18. The differece betwee the quatity idices due to Laspeyre ad Paasche is called: a) formula error b) samplig error c) homogeeity error d) oe of the above 19. If the idex umber is idepedet of the uits of measuremets, the it satisfies: a) times reversal test b) factor reversal test c) uit test d) all the above 20. The coditio for the time reversal test to hold good with usual otatios is: a) p01 p10 1 b) p10 p01 0 c) p01 / p10 1 d) p01 p Idex umber reveal the state of: a) iflatio b) deflatio c) both (a) ad (b) d) either (a) or (b) 22. Idex umber is a: a) measure of relative chages b) a special type of a average c) a percetage relative d) all the above 23. Data for idex umbers should be collected from: a) the retailers b) the wholesale dealers c) the selected group of persos d) oe of the above 24. Most preferred type of average for idex umber is: a) arithmetic mea b) geometric mea c) harmoic mea d) oe of the above 25. Most frequetly used idex umber formulae are: a) weighted formulae b) uweighted formulae c) fixed weight formulae d) oe of the above 26. Laspeyre s idex umber is also kow as: a) fixed base idex b) give year method idex c) base year method idex d) oe of the above 27. The weights used i Paasche s formula belog to: a) the base period b) the give period c) to ay arbitrary chose period d) oe of the above

7 28. Paasche was: a) a Eglish mathematicia b) a Frech ecoomist c) a Germa statisticia d) oe of the above 29. Paasche s idex umber was iveted i the year: a) 1871 b) 1901 c) 1874 d) If Laspeyre s price idex is 324 ad Paasche s price idex 144, the Fisher s ideal idex is: a) 234 b) 180 c) 216 d) oe of the above (28) a ANSWERS 1. d 2. c 3. d 4. c 5. b 6. a 7. c 8. b 9. c 1 0. a 1 1. c 1 2. b 13. d 1 4. b 1 5. c 1 6. d 1 7. c 1 8. a 1 9. c 2 0. a 2 1. c 2 2. d 2 3. d 2 4. b 2 5. a 2 6. c 2 7. b 2 8. c 2 9. c 3 0. c 6 1. (a) (b) ; ; ; Multiple Choice Questios Module - IV 1. Variatio i the items produced i a factory may be due to: (a) chace factors (c) both (a) ad (b) (b) assigable causes 2. Chace or radom variatio i the maufactured product is (a) cotrolable (c) both (a) ad (b) (b) ot cotrolable 3. Chace variatio i respect of quality cotrol of a product is (a) tolerable (c) ucotrolable (b) ot effectig the quality of a product 4. The causes leadig to vast variatio i the specificatios of a product are usually due to: (a) radom process (b) assigable causes (c) o-traceable causes 5. Variatio due to assigable causes i the product occurs due to: (a) faulty process (b) carelessess of operators (c) poor quality of raw material (d) 6. The faults due to assigable causes: all the above (a) ca be removed (b) caot be removed (c) ca sometimes be removed 7. Cotrol charts i statistical quality cotrol are meat for: (a) describig the patter of variatio (b) checkig whether the variability i the product is withi the tolerace limits or ot (c) ucoverig whether the variability i the product is due to assigable causes or ot

8 8. Cotrol charts cosist of: (a) three cotrol lies (b) upper ad lower cotrol limits (c) the level of the process 9. Mai tools of statistical quality cotrol are: (a) shewhart charts (c) both (a) ad (b) (b) acceptace samplig plas 10. The relatio betwee expected value of R ad S.D. with usual costat factors is. (a) E(R) = d 1 (b) E (R) = d 2 (c) E(R) = D1 (d) E (R) = D2 11. The cotrol limits for R-chart with a kow specified rage R ad usual costat factors are: U. C. L.( d3), d.. C L d ad (a) R 2 3 R R 1 R (b) L. C. L.( d3) d R 2 3 R U. C. L. D R, C. L. d ad R 2 R 2 R L. C. L. R D1 R (c) either (a) or (b) (d) either (a) or (b) 12. Whe the value of the populatio rage R is ot kow, the for X -chart, the trial cotrol limits with usual costat factors are: (a) U. C. L. X A3 R, C. L. X ad L. C. L. X A2 R (b) U. C. L. X A3 R, C. L. X ad L. C. L. X A2 R (c) U. C. L. A3 R, C. L. X ad L. C. L. A2 R (d) U. C. L. X A3 R, C. L. X ad L. C. L. X A3 R 13. The trial cotrol limits for R-chart with usual costat factors are: (a) U.C.L.= D 4 R, C.L.= R ad L.C.L. = D 3 R (b) U.C.L.= D 4 R,C.L.= R ad L.C.L. = D 3 R (c) U.C.L.= D 4 R, C.L.= R ad L.C.L. = D 4 R 14. R-charts are preferable over -charts because: (a) R ad S.D. fluctuate together i case of small samples (b) R is easily calculable (c) R-charts are ecoomical 15. The Shewhart cotrol charts are meat: (a) to detect whether the process is uder statistical quality cotrol (b) to fid the assigable causes (c) to reflect the selectio of samples

9 16. 3-sigma cotrol limits of defectives havig a give value of fractio defectives p are: (a) 3 p q U.C.L.,.. ad L.C.L.= 3 p q p C L p p (b) 1 pq U.C.L. p, C. L. pad 3 L.C.L.p 1 3 pq (c) U.C.L. p3 p q, C. L. pad L.C.L.= p 3 pq sigma trial cotrol limits with p as mea umber of defectives based o a sample of size are: (a) U. C. L.(1), p.. p p C L p ad L. C. L.(1) p p p (b) U. C. L. p 3(1), p.. p C L p ad L. C. L. p 3(1) p p (c) U. C. L. p 3(1), p.. p C L p ad L. C. L. p 3(1) p p sigma trial cotrol limits for c-chart for equal size samples are give as: (a) U. C. L. C 3 C, C. L. C ad L. C. L. C 3 C (b) U. C. L. C 2 C, C. L. 2C ad L. C. L. C 2C (c) U. C. L. C 2 C, C. L. C ad L. C. L. C 2 C (d) U. C. L. C 2 C, C. L. C ad L. C. L. C 2 C 19. If ad are the process mea ad S.D., the the cotrol limits 3 are kow as: (a) modified cotrol limits (b) atural cotrol limits (c) specified cotrol limits 20. The cotrol limits delimited by the cosumer are called: (a) modified cotrol limits (b) atural cotrol limits (c) specified cotrol limits

10 ANSWERS 1. c 2. b 3. d 4. b 5. d 6. a 7. d 8. a 9. c 1 0. b 1 1. c 1 2. d 1 3. b 1 4. d 1 5. d 1 6. c 1 7. b 1 8. a 1 9. b 2 0. c Q. No. CL UCL LCL Whether Uder Cotrol No Yes Yes Yes No Yes Yes Yes Yes No 6 8 The process is ot i a state of statistical cotrol because 4 th sample (p = 26/400 = 0.065) lies outside the cotrol limits 7 1 UCL = LCL = Sice all poits lie withi these limits, the process is i state of statistical cotrol.

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