MSG Sample Survey and Sampling Technique [Tinjauan Sampel & Teknik Persampelan]

Transcription

1 UIVERITI AI MAAYIA Frst emester Eamato 06/07 Academc esso December 06 / Jauar 07 MG ample urve ad amplg Techque [Tjaua ampel & Tekk Persampela] Durato : 3 hours [Masa : 3 jam] Please check that ths eamato paper cossts of THIRTEE pages of prted materal before ou beg the eamato. [la pastka bahawa kertas peperksaa megadug TIGA BEA muka surat ag bercetak sebelum ada memulaka peperksaa.] Istructos: Aswer all eght [8] questos. [Araha: Jawab semua lapa [8] soala.] I the evet of a dscrepaces, the Eglsh verso shall be used. [ekraa terdapat sebarag percaggaha pada soala peperksaa, vers Bahasa Iggers hedaklah dgua paka]. /-

2 - -. tate three dfferet tpes of o-samplg errors ad brefl descrbe crcumstaces surves that gve rse to these errors. Dscuss the two uses of ope versus closed questos. [ 0 marks ]. ataka tga jes ralat buka keraa pesampela da teragka secara rgkas keadaa dalam kaj seldk ag wujuda ralat tersebut. Bcagka dua keguaa soala terbuka berbadg soala tertutup. [ 0 markah ]. A toursm board Pesular Malasa has coducted a surve of small hotels (defed as hotels wth or fewer rooms). Oe of the objectves was to establsh the etet to whch small hotels used the local tourst formato ceter to obta bookgs. A smple radom samplg was coducted from a populato of 300 hotels. It was foud that of 60 resposes receved, 45 hotels used the local toursts formato ceter to obta bookgs. Determe a appromate 90% cofdece terval for the proportos of all small hotels the coutr whch use local tourst formato ceter to obta bookgs. Epla our results. Wth the same surve, hotel keepers were asked about ther room prces. The average prce of a sgle room was RM00 per ght ad the stadard devatos of prces was RM60. The research offcer was hopg to estmate the mea room prce to wth RM. Estmate the smallest acheved sample sze wth at least 95% cofdece. tate the two advatages ad dsadvatages for ths tpe of samplg. [ 0 marks ]. embaga pelacoga d emeajug Malasa telah mejalaka satu kaja terhadap hotel-hotel kecl (dtakrfka sebaga hotel dega blk ke bawah). alah satu objektf adalah utuk megetahu sejauh maa hotel kecl megguaka pusat maklumat pelacoga tempata utuk medapatka tempaha. atu pesampela rawak mudah dlaksaaka darpada populas sebaak 300 buah hotel. Ia medapat bahawa 60 maklum balas ag dterma, sebaak 45 hotel megguaka pusat maklumat pelacog tempata utuk medapatka tempaha. Tetuka aggara selag keaka 90% bag perkadara utuk semua hotel kecl d egara ag megguaka pusat maklumat pelacoga tempata utuk medapatka tempaha. 3/-

3 - 3 - Dalam kaja ag sama, pejaga hotel dtaa megea harga blk mereka. Harga purata sebuah blk perseoraga adalah RM00 utuk satu malam da ssha pawaa alah RM60. Pegawa peeldka berharap utuk megaggar m harga blk dalam lgkuga RM. Aggarka saz sampel ag terkecl ag boleh dcapa dega sekuragkuraga 95% keaka. ataka dua kebaka da keburuka utuk jes pesampela. [ 0 markah ] 3. Foresters wat to estmate the average age of trees a stad. I geeral, the older the tree, the larger the dameter, ad the dameter s eas to measure. The foresters measure the dameters of all 00 trees ad foud that the mea s 0.5 ad the the radoml select 5 trees for age measuremet. Tree umber Dameter, Age, (d) 57.6 ; 6050 ; Idetf the varable of terest, samplg ut ad a addtoal formato assocated wth the uts. Estmate the populato mea age of trees the stad usg rato estmato ad gve a appromate stadard error for our estmate. Determe a appromate 95% cofdece terval for the populato total age of trees the stad b usg regresso estmato. Compute the relatve effcec of the two estmators. Epla our result. [ 5 marks ] 3. Pegawas perhutaa g megaggarka m usa pokok d suatu kawasa. ecara umuma, pokok ag lebh tua, garspusata adalah lebar, da garspusat adalah mudah utuk dukur. Pegawas perhutaa megukur garspusat pada semua 00 pokok da ddapat bahawa m alah 0.5 da mereka kemuda memlh secara rawak 5 pokok utuk ukura usa. ombor pokok Garspusat, Usa, ; 6050 ; Camka pembolehubah ag damat, ut pesampela, da apa-apa maklumat tambaha ag berkata dega ut. 4/-

4 (d) Aggarka m populas usa pokok d kawasa tersebut dega megguaka sbah aggara da car ralat pawa utuk aggara ada. Tetuka aggara 95% selag keaka utuk jumlah populas usa pokok d kawasa tersebut dega megguaka regres aggara. Kraka kecekapa relatf bag kedua-dua pegaggar. Teragka jawapa ada. [ 5 markah ] 4. There are 300 pods a developmet block cosstg of 0 vllages. The admstrato s plag to use these pods for fsh farmg. A surve was udertake to estmate the total pod area avalable at preset. A smple radom sample of 8 vllages was draw. The area of each pod the sample vllages was accuratel measured. The umber of pods each sampled vllages ad the area of pods are as follows: Vllage umber of pods Area ( hectares) tate the tpe of samplg desg used. Estmate the total pod area the developmet block, ad place a boud o the error of estmato. How ma vllages should be cluded the sample for estmatg populato total wth a marg of error of magtude 60 hectares? [ 4 marks ] 5/-

5 Terdapat sebaak 300 buah kolam d blok pembagua ag terdr darpada 0 buah kampug. Pusat petadbra meracag utuk megguaka kolam utuk teraka ka. atu kaja telah djalaka utuk megaggar jumlah luas kawasa ag seda ada. atu sampel sebaak 8 buah kampug telah dplh secara rawak mudah. uas bag setap kolam d kampug ag terplh dukur dega tepat. Blaga kolam d setap kampug ag dsampelka da luas kawasa kolam adalah sepert berkut: Kampug Blaga kolam uas (dalam hektar) ataka jes reka betuk pesampela ag dguaka. Aggarka jumlah luas kawasa kolam d blok pembagua, da tetuka batas ralat pegaggara. Berapa baak kampug ag perlu dsampelka utuk megaggar jumlah luas kawasa kolam dega batas 60 hektar bag ralat pegaggara? [ 4 markah ] 5. I 00, researchers a Govermet Departmet wshed to eame the degree of abseteesm amogst emploees. As t was tme cosumg, the researchers took a sample of persoel records, wth the stratfcato beg b pa grade The results are summarzed below. Pa grade umber of emploees ample sze Mea sample of das of absece Varace sample Hgh Mddle ow Estmate the mea umber of das of absece for all emploees. Estmate the stadard error of the mea umber of das of absece for each of the three pa grades. Calculate a appromate 95% cofdece terval for the total umber of das of absece for all emploees. 6/-

6 (d) I 0, researchers are to repeat the vestgato to determe whether the abseteesm rate has mproved. Ths would use formato from 00, ad a total sample sze of 0. Fd the values of h that gve optmal allocato, ad epla wh such allocato mght be beefcal ths stud. [ 7 marks ] 5. Pada tahu 00, peeldk d sebuah Jabata Kerajaa g memerksa tahap ketdakhadra dalam kalaga pekerja. Oleh sebab a aka memaka masa, peeldk megambl sampel rekod kaktaga, dega stratfkas dlakuka megkut gred gaj. Keputusa drgkaska sepert berkut: Gred gaj Blaga kaktaga az sampel ampel m bag blaga har tdak hadr Tgg ederhaa Redah ampel varas (d) Aggarka m blaga har ag tdak hadr utuk semua kaktaga. Aggarka ralat pawa bag m blaga har ag tdak hadr bag setap gred gaj. Kra aggara 95% selag keaka bag jumlah blaga har ag tdak hadr utuk semua kaktaga. Pada tahu 0, peeldk megulag sasata utuk meetuka sama ada kadar ketdakhadra telah bertambah bak. Car la h ag member perutuka ag optmum, da jelaska keapa perutuka mugk member mafaat dalam kaja. [ 7 markah ] 6. PERMATA s a compa sellg electrcal equpmet ad supples to electrcas, cotractors, ad other wholesale customers. The tems are stored stacks whch are lke large bookcases ecept that the have bs stead of shelves. The PERMATA s warehouse cotas 400 stacks of the same shape ad sze, ad there are about 6,000 bs. uppose that 4 stacks are selected at radom. The relevat formato s show below: elected tack Total umber of Bs umber of elected Bs ad Items umber of Items wth a Dscrepac tate the tpe of samplg desg used. Estmate the total umber of tems the warehouse wth a dscrepac. Place a boud o the error of estmato. [ marks ] 7/-

7 PERMATA alah sebuah sarkat ag mejual peralata eletrk da membekalka kepada jurueletrk, kotraktor, da pembel la ag membel secara borog. Item-tem ag dsmpa dalam susua sepert sebuah rak buku ag besar kecual a mempua bekas ag besar da bukaa rak. Gudag PERMATA megadug 400 susua ag sama saz da betuk, da terdapat sebaak 6,000 bekas besar. Adaka 4 susua dplh secara rawak. Iformas ag berkata dtujukka dalam jadual ag berkut: usua terplh Jumlah Bekas Besar Blaga Bekas Besar Terplh da Item Blaga Item ag Berbeza ataka jes reka betuk pesampela ag dguaka. Aggarka jumlah blaga tem dalam gudag ag berbeza. Tetuka batas ralat pegaggaraa. [ markah ] 7. From the lst of 0 workers Table, use repeated sstematc samplg to take a total sample of 0 workers for purposes of estmatg mea umber of work das loss due to acute lless b all workers. The obta 90% cofdece terval for the estmates. uppose that the radom umbers chose are 4, 4, 30,, 7 [ marks ] 7. Darpada seara 0 pekerja dalam Jadual, guaka persampela sstematk berulag utuk memlh sejumlah sampel serama 0 orag pekerja ag bertujua utuk megaggarka m blaga har bekerja ag rug akbat peakt ag teruk oleh semua pekerja. eterusa dapatka 90% selag keaka bag aggara tersebut. Adaka ombor rawak ag terplh adalah 4, 4, 30,, 7 [ marks ] 8/-

8 - 8 - Table : Das oss from Work because of Acute Illess Oe Year Amog 0 Emploee a Plat Jadual : Blaga Har Bekerja ag Rug Akbat Peakt ag Teruk dalam atu Tahu bag 0 Pekerja d sebuah Klag Emploee ID ID Pekerja Das ost Emploee ID Das ost Emploee ID Das ost Har ag Rug ID Pekerja Har ag Rug ID Pekerja Har ag Rug 9/-

9 For a smple radom samplg wthout replacemet, show that the probablt of a elemet beg selected to a sample s Uder proportoal allocato, the sample sze stratum h s h h h h how that V ( ) st h h h h h h [ 0 marks ] 8. Utuk pesampela rawk mudah tapa peggata, tujukka bahawa kebaragkala satu eleme ag terplh ke dalam sampel alah Bag perutuka berkadara, saz sampel dalam strata h alah h h h h Tujukka bahawa V ( ) st h h h h h h [ 0 markah ] 0/-

10 - 0 - Apped /ampra ample ample varace, s s ( ) ( ) s a ˆ ˆ p p s ˆ p ˆ ˆ p p r, b b b ( ) b d d d m m M /-

11 - - ampel ample Varace a m M p wth p µ pm ( a ) m M M M t wth t ( t ) M m b M M M M m ˆ M M wth b m j j M M ˆ m MB m MW m M m ˆ r M M M m r M M M M m wth r M ˆ M r /-

12 - - ample ample varace pˆ Mpˆ M M ˆˆ m pq r M M M M m wth r M pˆ pm ˆ 3/-

13 - 3 - ample ze ; D B ; D B D 4 4 D w ; w kk Ck C k D C C ; D ; D ( C C ) / C o, C Optmal Allocato ema Allocato Proportoal Allocato pq w pq c ; D pq pq c B B B D D D D r t p ; ; ; D D D ; ; ; r t p B M B D ; D 4 4 Itra class correlato coeffcet k w j u k ju - ooo O ooo -