STA 105-M BASIC STATISTICS (This is a multiple choice paper.)

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1 DCDM BUSINESS SCHOOL September Mock Eamatos STA 0-M BASIC STATISTICS (Ths s a multple choce paper.) Tme: hours 0 mutes INSTRUCTIONS TO CANDIDATES Do ot ope ths questo paper utl you have bee told to do so by the vglator. The marks awarded for each questo are dcated brackets []. All workgs must be very clearly show ad all dagrams must be well labelled. Slet electroc (o-programmable scetfc) calculators may be used. The total umber of marks avalable s 00. Aswer ALL questos. You wll fd a lst of formulae o page 0. Normal ad t-tables are also provded o pages ad. Ths questo paper cossts of prted pages. Eamer: Rajesh Guesh Page of STA0-M SEP00

2 . Varables whch measuremet s always appromate because they permt a ulmted umber of termedate values are () Nomal. () Dscrete. () Ordal. (4) Cotuous. () Iterval.. Whch of the followg radom varables are cotuous ad whch are dscrete? I IQ II Number of kttes a ltter. III Number of resposes made by a rat a bar-pressg stuato. IV The rate of bar pressg (resposes per ut tme). () I ad II cotuous; III a IV dscrete. () I, III ad IV cotuous; II dscrete. () IV cotuous; I, II ad III dscrete. (4) I cotuous, II, III ad IV dscrete. () Noe of the above s correct. [] []. For a daytme house-to-house survey to study wome's atttudes about ther role socety, whch oe of the followg errors would be most lkely to occur? () Reportg ad processg errors. () Itervewer bas. () No-respose. (4) False formato by the respodets. 4. Cosder the followg data: The varace for the above populato s () 0. ().4 () 6 (4) 8. [] [] Eamer: Rajesh Guesh Page of STA0-M SEP00

3 . Cosder the followg data: y 67 ( y y) 08 The sample mea ad varace are respectvely () 67. ad 98.4 () 6.0 ad 98.4 () 6.0 ad 08. (4) 67. ad The heghts of a sample of te people are Whch are the correct real lmts for the frequecy table gve below? (a) (b) (c) Frequecy () Colum (a) s correct. () Colum (b) s correct. () Colum (c) s correct. (4) All of colums (a), (b) ad (c) are correct. () Noe of colums (a), (b), ad (c) are correct. 7. The mea of the data the gve table s () 9 () 9 () 9 4 (4) Frequecy Eamer: Rajesh Guesh Page of STA0-M SEP00

4 8. For a symmetrc dstrbuto, whch statemet s true about ts mea ad meda? () They are the same. () They are always dfferet. () Sometmes they are the same but sometmes they are dfferet. (4) There s ot eough formato to establsh ths fact. [] 9. A dstrbuto of 6 scores has a meda of. If the hghest score creases by pots, whch statemet s true about the resultg value of the meda? () It remas. () It creases to. () It creases to 4. (4) It caot be determed wthout addtoal formato. [] 0. A smple radom sample s oe where () You decde o a sample se ad sample proportoately from the populato. () You choose each tem wth o regard to prevous choces. () Each tem the populato has a equal chace of beg chose. (4) All of the above are true. () Noe of the above s true.. A populato of se 0 s dvded to three strata of ses 00, 0 ad 0 wth respectve varaces 4, 9 ad 6. A radom sample of se s draw from ths populato usg optmal allocato. The varace of the sample mea s [] () 0.47 ().0 () (4) 0.4 (). [6]. A card s draw from a stadard -card deck. I descrbg the occurrece of two possble evets, a Ace ad a Kg, these two evets are sad to be () Idepedet. () Mutually eclusve. () Radom varables. (4) Radomly depedet. [] Eamer: Rajesh Guesh Page 4 of STA0-M SEP00

5 . Amog twety-fve artcles, e are defectve, s havg oly mor defects ad three havg major defects. Determe the probablty that a artcle selected at radom has major defects gve that t has defects. () () 0. () 0.4 (4) () [Questos 4 7 refer to the followg problem.] The depostors at Save-More Bak are categored by age ad se. A dvdual s selected at radom from ths group of 000 depostors. SEX AGE Male Female 0 or less or more The probablty that the dvdual s a female s () 0 () () (4) []. The probablty that the depostor s a female aged 0 or less s () () 4 () 7 (4) 0 [] Eamer: Rajesh Guesh Page of STA0-M SEP00

6 6. The probablty that the depostor s a male or s aged or more s () () 0 () (4) The codtoal probablty that the depostor draw s 0 or less, gve that he s a male s () 7 () 0 () 4 7 (4) 8. What uder the stadard ormal curve falls outsde the -values. ad.? () () () (4) () [] 9. Oe hudred studets took a test o whch the mea score was 7 wth a varace of 64. A grade of A was gve to all who scored 8 or better. Appromately how may A's were there, assumg scores were ormally dstrbuted? (Choose the closest.) () 4 () 7 () 8 (4) () Eamer: Rajesh Guesh Page 6 of STA0-M SEP00

7 0. If the se of the sample beg used s creased, the whch of the followg statemets s true about the wdth of a 9% cofdece terval estmate for the populato mea? () It wll become arrower. () It wll become wder. () It wll rema the same. (4) The effect o the wdth caot be determed from the gve formato.. The populato mea competecy score for all Famly Nurse Practtoers (FNP' s) s µ ad the populato varace s 00. If a sample of 6 FNP' s from several smlar type hosptal clcs s selected ad the mea competecy score s 80, the mddle 99% pots for the dstrbuto of the sample mea competecy wll be (rouded to two decmal places) () (4.4, 0.76) () (76., 8.88) () (6.74, 0.6) (4) (7.7, 84.9). To fd cofdece tervals for the mea of a ormal dstrbuto, the t-dstrbuto s usually used stead of the stadard ormal dstrbuto because () The mea of the populato s ot kow. () The t-dstrbuto s more effcet. () The varace of the populato s usually ot kow. (4) The stadard error of the estmate s s. () The sample mea s kow.. A sample of 600 cases s draw at radom from a ftely large populato. The stadard devato of the populato s 0. The stadard error of the mea s [] [] [] () () 6 () 4 (4) 0 [] Eamer: Rajesh Guesh Page 7 of STA0-M SEP00

8 4. What s the probablty of a Type II error whe α 0. 0? () 0.0 () 0.00 () 0.90 (4) 0.97 () It caot be determed wthout more formato. []. For what level of cofdece do we use.6449, for a two-sded test or cofdece terval? () 90 % () 9 % () 80 % (4) 00 % () 99 % [] 6. I testg H 0 : µ 0 agast H : µ > 0 wth α 0. 0,, s 6 ad, oe should coclude that () µ > 0 wth % chace of error. () µ > 0 wth % cofdece. () µ 0 wth 9% cofdece. (4) µ 0 wth 9% chace of error. [] 7. A pocket calculator ethusast clams that 80% of all comg freshme ow a pocket calculator. To vestgate ths clam, a radom sample of 00 comg freshme have bee tervewed. Of these, 48 ow calculators. If we were to test the ull hypothess H 0 : p 0. 8 s tested agast a two-taled alteratve H : p 0. 8, the decso based o the sample data would be 0 () Accept H 0 at the 0 % sgfcace level. () Accept H 0 at the % sgfcace level. () Reject H at the % sgfcace level. (4) Reject H 0 at the % sgfcace level. [] Eamer: Rajesh Guesh Page 8 of STA0-M SEP00

9 8. The correlato coeffcet for X ad Y s kow to be ero. We the ca coclude that () X ad Y have stadard dstrbutos. () The varaces of X ad Y are equal. () There ests o relatoshp betwee X ad Y. (4) There ests o lear relatoshp betwee X ad Y. 9. Whch of the followg values of r dcates the most accurate predcto of oe varable from aother? () r.8 () r 0.77 () r 0.68 (4) r 0.97 () r. 0. A bak s epermetg wth the umber of cashers t has o duty. Spot checks are made at radom tmes of the day ad the umber of cashers ad the umber of customers watg for servce the queue at that tme are recorded as follows: [] [] Number of cashers, X Number of customers, Y For the above set of pared data, whch statemet s correct? () 9, 4, y 0 () The lear correlato coeffcet betwee X ad Y s () The covarace betwee X ad Y s.0. (4) If the umber of cashers s 6, the epected umber of customers wll be appromately.. () The equato of the regresso le of Y o X s Y X. [6] Eamer: Rajesh Guesh Page 9 of STA0-M SEP00

10 LIST OF FORMULAE Dscrete data Sample mea Sample varace ) ( s Grouped data Sample mea f f Sample varace ) ( f s Optmal allocato r N N N N ] var[ σ NORMAL AND STUDENT S t DISTRIBUTIONS σ µ s t INFERENTIAL STATISTICS Testg for mea σ µ Testg for mea (t-test) s t µ Testg for proporto p p p p ) ( ˆ REGRESSION AND CORRELATION Regresso coeffcets ( ) y y b b y a Covarace Correlato coeffcet ], [ y y Y X Cov ( ) { } ( ) { } y y y y r Eamer: Rajesh Guesh Page 0 of STA0-M SEP00

11 Left, rght ad cetral probabltes of the stadard ormal dstrbuto Left Rght Cetral Left Rght Cetral Left had Rght had Cetral Crtcal values of the stadard ormal dstrbuto Left Rght Cetral Left Rght Cetral Eamer: Rajesh Guesh Page of STA0-M SEP00

12 Crtcal values of the t-dstrbuto wth f degrees of freedom Degrees of Probablty ( α ) freedom f Oe-sded Two-sded Eamer: Rajesh Guesh Page of STA0-M SEP00

Summary of the lecture in Biostatistics

Summary of the lecture in Biostatistics Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the