MSG 368 Sample Survey and Sampling Technique [Tinjauan Sampel dan Teknik Pensampelan]

Transcription

1 UIVERSITI SAIS MAAYSIA Secod Semester Eamato 0/0 Academc Sesso Jue 0 MSG 368 Sample Surve ad Samplg Techque [Tjaua Sampel da Tekk Pesampela] Durato : 3 hours [Masa : 3 jam] Please check that ths eamato paper cossts of TWEVE pages of prted materals before ou beg the eamato. [Sla pastka bahawa kertas peperksaa megadug DUA BEAS muka surat ag bercetak sebelum ada memulaka peperksaa.] Istructos: [Araha: Aswer all te [0] questos. Jawab semua sepuluh [0] soala.] I the evet of a dscrepaces, the Eglsh verso shall be used. [Sekraa terdapat sebarag percaggaha pada soala peperksaa, vers Bahasa Iggers hedaklah dgua paka]. /-

2 - - [MSG 368]. Cosder the problem of measurg the wgspa of bats a certa rego. I ths rego there are three speces of bats : hoav, slver-hared, ad red. et p k = proporto of bats the k th subpopulato that have a wgspa greater tha 5 ches. The vestgator beleves that appromatel 30 bats lve the area. Of the 30 bats captured, are from the frst speces uder stud ad 3 of these have a wgspa greater tha 5 ches. (a) Estmate p. Determe the boud o error of estmato. (c) Obta the 90% cofdece terval for p. [0 marks]. Pertmbagka masalah megukur lebar saap kelawar d suatu kawasa tertetu. D kawasa tersebut terdapat tga jes kelawar: hoav, berbulu perak, da merah. Barka p k = kadara kelawar dalam subpopulas ke-k ag mempua lebar saap ag lebh besar darpada 5 c. Peasat percaa bahawa kra-kra 300 kelawar berada d kawasa tu. Darpada 30 kelawar ag dtagkap, darpadaa adalah jes pertama d bawah kaja da 3 mempua lebar saap ag lebh besar darpada 5 c. (a) Aggarka p. Tetuka aggara batas ralata. (c) Dapatka selag keaka 95% bag p. [0 markah]. (a) State the methods of data collecto. Select two of them ad gve two advatages ad two dsadvatages of each. Defe the followg terms: () Target populato () Samplg frame () Samplg Bas (v) Samplg error [0 marks]. (a) Apakah kaedah-kaedah pegumpula data?. Plh dua darpadaa da berka dua kebaka da dua keburuka bag setap satua. Takrfka sebuta-sebuta ag berkut: () Populas sasara () Keragka pesampela () Pesampela berat sebelah (v) Pesampela ralat [0 markah] 3/-

3 - 3 - [MSG 368] 3. I smple radom samplg wthout replacemet where uts are selected from uts, show that (a) the probablt that the th ut s selected o the k th draw s. Var( ) wth, ( ) [5 marks] 3. Dalam pesampela rawak rgkas tapa peggata dega ut dplh darpada ut, tujukka bahawa (a) kebaragkala bahawa ut dplh pada cabuta ke-k alah. Var( ) dega, ( ) [5 markah] 4. There s a relatoshp betwee the come of a household ad the total floor space of the home of a household a certa rego of Sarawak. A smple radom sample of sze 4 has bee selected wthout replacemet. The table below cotas the sample data. Household 3 4 Floor space Icome Gve ; 3547 ; The mea floor space of all houses the populato s 03.7 m. (a) Compute the rato estmator for the mea come. Compute the regresso estmator for the mea come. (c) Whch of the two methods, parts (a) or, s most approprate ths case? Wh? [5 marks] 4/-

4 - 4 - [MSG 368] 4. Terdapat hubuga atara pedapata s rumah da jumlah ruag lata rumah bag satu s rumah d ratau ag tertetu d Sarawak. Satu sampel rawak rgkas ag bersaz 4 telah dplh tapa peggata. Jadual d bawah megadug data sampel. Isrumah 3 4 Ruag lata Pedapata Dber ; 3547 ; M ruag lata bag semua rumah dalam populas alah 03.7 m. (a) Kraka pegaggar sbah bag m pedapata. Kraka pegaggar regres bag m pedapata. (c) Yag maakah atara kedua-dua kaedah, d bahaga (a) atau palg sesua dalam kes? Keapa? [5 markah] 5. A uverst has 807 facult members. For each facult member, the umber of referred publcatos was recorded. The followg data are from a sample of facult, usg the areas bologcal sceces, phscal sceces, socal sceces, ad humates as the strata. Stratum umber of Facult Members Stratum umber of Facult members Sample Bologcal Sceces 0 7 Phscal Sceces 30 9 Socal Sceces 7 3 Humates 78 Total The frequec table for umber of publcatos the strata s gve below. umber of umber of Facult Members Referred Publcatos Bologcal Phscal Socal Humates /-

5 - 5 - [MSG 368] (a) Estmate the total umber of referred publcatos b facult members the uverst, ad gve the stadard error. Estmate the proporto of facult wth o referred publcatos, ad determe the boud o the error of estmato. Epla our results. [5 marks] 5. Sebuah uverst mempua 807 ahl fakult. Bag setap ahl fakult, blaga peerbta ag drujuk telah drekodka. Data berkut adalah darpada sampel fakult, dega megguaka bdag sas bolog, sas fzkal, sas sosal, da sas kemasarakata sebaga strata. Stratum Blaga Ahl Fakult dalam Stratum Blaga Ahl Fakult dalam Sampel Sas Bolog 0 7 Sas Fzkal 30 9 Sas Sosal 7 3 Kemasarakata 78 Jumlah Jadual frekues bag blaga peerbta dalam strata adalah sepert d bawah. Blaga Blaga Ahl Fakult Peerbta Yag Drujuk Bolog Fzkal Sosal Kemasarakata (a) Aggarka jumlah peerbta ag drujuk oleh ahl fakult d uverst, da berka ralat pawa. Aggarka kadara fakult ag tada peerbta ag drujuk, da tetuka batas ralat pegaggara. Jelaska jawapa ada. [5 markah] 6/-

6 - 6 - [MSG 368] 6. The ew cad Gree Sweet s beg test-marketed the areas of Selagor ad Johore. The market research frm decded to sample 6 ctes from the 45 ctes the areas ad the to sample supermarkets wth ctes, order to kow the umber of cases of Gree Sweet sold. Ct umber of Supermarkets umber of cases sold 5 46, 80, 5, 5, 7, 8, 7, 36, 73, , 0, 5, , 79, 98, 63, 6, 87, , 9, 57, 46, 86, 43, 85, , , 43, 59 (a) (c) (d) State the tpe of samplg desg used. State the prmar samplg uts ad secodar samplg uts. Estmate the total umber of cases sold ad place the boud o the error of estmato. Estmate the average umber sold per supermarket. Determe the stadard error of our estmates. [35 markah] 6. Gula-gula baru Gree Sweet sedag dpasarka d kawasa Selagor da Johor. Frma peeldka pasara telah memutuska utuk mecuba 6 badar raa darpada 45 badar raa d kawasa-kawasa tersebut da kemuda aka mesampelka pasar raa dalam badar raa terplh supaa megetahu blaga kes Gree Sweet ag telah djual. Badar raa Blaga Pasar raa Blaga kes ag djual 5 46, 80, 5, 5, 7, 8, 7, 36, 73, , 0, 5, , 79, 98, 63, 6, 87, , 9, 57, 46, 86, 43, 85, , , 43, 59 (a) ataka jes reka betuk pesampela ag dguaka. ataka ut pesampela utama da ut pesampela kedua. (c) Aggarka jumlah kes-kes ag djual da tetuka batas ralat pegaggara. (d) Aggarka m blaga ag djual pada setap pasar raa. Tetuka ralat pawa bag pegaggara ada. [35 markah] 7/-

7 - 7 - [MSG 368] 7. A samplg desg was coducted a large ct Cha. The ct comprses s dstrcts. Wth each dstrct, a smple radom sample of two eghborhood groups were selected, ad all dvduals wth each eghborhood group were tervewed cocerg ther overall health status. The followg table represets data from the surve o the umber of dvduals over 30 ears of age who were edetulous (havg lost teeth). Dstrct,, 4, ad 6 each cota 00 eghborhood groups; dstrct 3 cotas 75 eghborhood groups; ad dstrct 5 cotas 50 eghborhood groups. The data are as follows: (a) Dstrct eghborhood Group umber of Persos > 30 ears umber of Edetulous Persos State the tpe of samplg desg used. Estmate ad costruct 95% cofdece terval for the total umber of edetulous. [5 marks] 7. Satu reka betuk pesampela telah djalaka d sebuah badar besar d Cha. Badar terdr darpada eam daerah. Dalam setap daerah, dua kumpula kejraa telah dplh secara sampel rawak rgkas, da kesemua dvdu dalam kumpula setap kejraa telah dtemubual berkeaa status keshata secara keseluruha. Jadual berkut mewakl data darpada kaja terhadap blaga dvdu ag lebh darpada 30 tahu ag edetulous (kehlaga gg). Daerah,, 4, da 6 setapa megadug 00 kumpula kejraa; daerah 3 megadug 75 kumpula kejraa; da daerah 5 megadug 50 kumpula kejraa. Data adalah sepert ag berukut: Daerah Kumpula Kejraa Blaga Idvdu > 30 tahu Blaga Idvdu ag Edetulous /-

8 - 8 - [MSG 368] (a) ataka jes reka betuk pesampela ag dguaka. Aggarka da baka selag keaka 95% bag jumlah blaga edetulous. [5 markah] 8. (a) Descrbe the three tpes of populato order to choose betwee sstematc ad smple radom samplg. Crop eld for a large feld of wheat s to be estmated b samplg small plots wth the feld whle the gra s rpeg. The feld s o slopg lad wth hgher fertlt towards the lower sde. Do ou thk smple radom samplg or sstematc radom samplg wll be effectve estmatg τ, the total wheat eld? Provde a detaled eplaato. [5 marks] 8. (a) Huraka tga jes populas utuk memlh atara pesampela sstematk da rawak mudah. Hasl taama bag sebuah ladag gadum adalah daggarka dega mesampelka plot-plot kecl dalam ladag semetara meuggu bjr masak. adag tersebut berada pada taah berceru dega kesubura ag lebh tgg ke arah bahaga bawah. Pada fkra ada adakah pesampela rawak mudah atau pesampela rawak sstematk aka berkesa dalam megaggarka, jumlah hasl gadum? Berka pejelasa ag terperc. [5 markah] 9. If term h s gored relatve to ut, show that Var ( ) Var ( ) optmum st proportoal st [5 marks] 9. Jka sebuta h dabaka relatf kepada ut, tujukka bahawa Var ( ) Var ( ) optmum st proportoal st [5 markah] 9/-

9 - 9 - [MSG 368] 0. A researcher would lke to coduct a stratfed radom samplg from a populato. If the cost surve fucto s the form of C = C 0 + C where C = RM0,000 ad C 0 = RM 4,000, determe the sample sze to be take from each stratum gve the followg formato: Stratum C S [5 marks] 0. Seorag peeldk g mejalaka pesampela rawak berstrata darpada satu populas. Jka fugs kos peeldka adalah dalam betuk dega C = C 0 + C C = RM 0,000 ad C 0 = RM 4,000, tetuka saz sampel ag dambl darpada setap stratum dega maklumat ag dber sepert berkut: Stratum C S [5 markah] 0/-

10 - 0 - [MSG 368] Apped Sample Sampel varace, s s s a ˆ ˆ p p s ˆ p ˆ ˆ p p r, b b b ( ) S b S d d d m m M /-

11 - - [MSG 368] Sampel Sample Varace a m M a ˆ pm m M M M t S wth S t ( t ) M m S S b M M M M m ˆ M M wth S S b m j M ˆ M j m ˆ r pˆ M M Mpˆ M M m S S r M M M M m wth S r M ˆ M r M ˆˆ m pq S r M M M M m wth S r M pˆ pm ˆ /-

12 - - [MSG 368] Sample Sze ; D B ; D B D 4 4 w D ; w kk Ck C k D C C ( C C ) / C o, C Optmal Allocato ; D ema Allocato ; D Proportoal Allocato pq a pq c ; D pq pq c ; B D ; D B ; D B D M B D D D r B ; ; r ooo O ooo -