UNIVERSITI SAINS MALAYSIA Peperiksaa Semester Kedua Sidag Akademik 006/007 April 007 HGT 19 KAEDAH KUANTITATIF DAN ANALISIS RUANGAN Masa : 3 jam Sila pastika bahawa kertas peperiksaa ii megadugi EMPAT BELAS muka surat yag bercetak sebelum ada memulaka peperiksaa ii. Jawab EMPAT soala. Jawab DUA soala dari setiap Bahagia A da B. /-
[HGT 19] - - Bahagia A 1. Dalam satu soal selidik yag dijalaka di sebuah kilag di Seberag Perai, didapati staf yag bekerja di kilag tersebut terbahagi kepada 40 orag di bahagia pegeluara, 100 orag di bahagia juala, da 60 orag di bahagia petadbira. [a] Jika sekiraya mi umur 400 orag staf dalam syarikat itu ialah 30.6 tahu, maakala mi umur bagi staf di bahagia pegeluara da juala ialah 7.6 da 3.1. Kira mi umur bagi staf bahagia petadbira. [5 markah] [b] Syarikat tersebut kemudiaya igi membuat aalisis tetag prestasi juala barag-barag syarikatya. Satu sampel 500 juala telah dipilih secara rawak da jadual berikut diperolehi: Jadual 1. Sampel peratusa ilai juala barag-barag syarikat. Nilai Juala Peratusa Juala 0-0 35 0-40 30 40-60 1 60-100 10 100-00 4 Kira sisiha piawai da persembahka data di atas dalam betuk grafik. [0 markah]. Jadual berikut meujuka peratusa pelajar waita yag berijazah daripada Uiversiti YZ dari tahu 1980 higga 007. Jadual.: Peratusa pelajar waita Uiversiti YZ yag berijazah 1980-007. Tahu 1980 1983 1986 1989 199 1995 000 004 007 % pelajar waita 56.4 58.8 60.7 64.4 64.1 64. 65.7 67.8 69.4 berijazah Jumlah kemasuka pelajar 000 500 3000 3500 4000 4500 5000 5500 6000 3/-
[HGT 19] - 3 - [a] [b] Kira persamaa regresi da plot poi da garisa di atas kertas graf. Berdasarka persamaa regresi itu, ramalka peratusa pelajar waita yag aka berijazah pada tahu berikutya apabila jumlah pelajar meigkat kapada 7000 orag. [5 markah] 3. Data Jabata Statistik Negara meujukka 63.9% populasi adalah berkahwi, 7.7% jada da duda, 6.9% bercerai (tidak berkahwi semula), da 1.5% bujag. Satu sampel 500 orag dewasa diambil daripada kalaga peduduk Lagkawi meujukka 310 berkahwi, 40 jada atau duda, 30 bercerai, da 10 bujag. Pada aras keyakia 95% ( α 0.05), buat koklusi sama ada peragkaa peduduk kawasa Lagkawi berbeza dega Negara? [5 markah] 4. Amau (ppm) satu baha laruta yag hadir dalam dua tahap kedalama taih (Jadual). Berdasarka data tersebut bolehkah ada membuat koklusi bahawa tiada terdapat perbezaa amau baha laruta tersebut di kedua-dua kedalama taih itu. Nyataka hipotesis ada da guaka aras keyakia 95% ( α 0.05). [5 markah] Jadual. Baha laruta (ppm) yag terdapat dalam dua tahap kedalama taih. 0 cm 40 cm 9 98 81 100 75 79 77 80 90 8 77 8 84 4/-
[HGT 19] - 4 - Bahagia B 5. Peta 1 meujukka tabura kes deggi di Lembaga Sg. Piag pada tahu 004 da Jadual 1 meujukka rigkasa aalisis yag telah dijalaka terhadap tabura tersebut. Berdasarka haya kepada maklumat yag diberika dalam peta da jadual tersebut, jawab soala berikut: [a] Jelaska kaedah yag diguaka dalam aalisis ii da uji kesigifikaa statistik corak ruaga tabura kes deggi berkeaa. [10 markah] [b] Huraika dapata ada. [5 markah] [c] Huraika batasa-batasa kaedah yag diguaka. [10 markah] Jadual 1: Rigkasa aalisis corak titik kes deggi di Lembaga Sg. Piag pada tahu 004. Keteraga Nilai Bilaga kes 118 Mi 1.18 Varia 8.65 6. Peta meujukka tabura lokasi tapak arkeologi di Lembah Bujag da Jadual meujukka rigkasa aalisis yag telah dijalaka terhadap corak tersebut. Berdasarka haya kepada maklumat yag diberika dalam peta da jadual tersebut, jawab soala berikut: [a] Megguaka kaedah yag sesuai, ukurka da uji kesigifikaa statistik corak ruaga tabura tapak arkeologi tersebut [10 markah] [b] Huraika dapata ada. [5 markah] [c] Huraika batasa-batasa kaedah yag diguaka. [10 markah] 5/-
[HGT 19] - 5 - Jadual : Rigkasa aalisis corak titik tapak arkeologi di Lembah Bujag. Keteraga Nilai Bilaga kes () 47 Keluasa 400 km persegi Purata jarak sebear ( NNND ) 5363.9 meter Purata jarak jagkaa ( NNND R ) 555.6 meter Ralat piawai ( σ ) 6.533 NND 7. [a] Huraika kompoe-kompoe aalisis ruaga. [10 markah] [b] Huraika keragka asas aalisis ruaga. [15 markah] 8. Berdasarka kepada cotoh-cotoh yag sesuai, bicagka sejauhmaa peraa sistem maklumat geografi dalam aalisis ruaga. [5 markah] Peta 1. Tabura Lokasi Kes Deggi di Lembaga Sg. Piag 6/-
[HGT 19] - 6 - N 0 Kilometers Peta. Tabura tapak arkeologi di Lembah Bujag. 7/-
[HGT 19] - 7 - Formula da Jadual z, t, da Chi Gada Dua : z s μ / t s μ / N N σ t s p + 1 1 1 1 s s s p 1 1 1 1 1 + + ( ) ( ) t d s d / Error! Bookmark ot defied. 1 ) ( s 1 ) ( s σ μ ( ) N [ ] ( ) ( ) [ ] ) ( ) ( ) )( ( ) ( Y Y Y Y r Atau, r (i )(Yi Y) (i ) (Yi Y ) 8/-
[HGT 19] - 8 - t r 1 r b a ( Y ) ( )( Y ( ) ( ) Y b ) Atau, a Y - b b ( i )( Yi Y) (i ) x 0 ( f f ) f e e 9/-
[HGT 19] Jadual Z (Stadard Normal (Z) Table) - 9 - Area betwee 0 ad z 0.00 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.0000 0.0040 0.0080 0.010 0.0160 0.0199 0.039 0.079 0.0319 0.0359 0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753 0. 0.0793 0.083 0.0871 0.0910 0.0948 0.0987 0.106 0.1064 0.1103 0.1141 0.3 0.1179 0.117 0.155 0.193 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517 0.4 0.1554 0.1591 0.168 0.1664 0.1700 0.1736 0.177 0.1808 0.1844 0.1879 0.5 0.1915 0.1950 0.1985 0.019 0.054 0.088 0.13 0.157 0.190 0.4 0.6 0.57 0.91 0.34 0.357 0.389 0.4 0.454 0.486 0.517 0.549 0.7 0.580 0.611 0.64 0.673 0.704 0.734 0.764 0.794 0.83 0.85 0.8 0.881 0.910 0.939 0.967 0.995 0.303 0.3051 0.3078 0.3106 0.3133 0.9 0.3159 0.3186 0.31 0.338 0.364 0.389 0.3315 0.3340 0.3365 0.3389 1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.361 1.1 0.3643 0.3665 0.3686 0.3708 0.379 0.3749 0.3770 0.3790 0.3810 0.3830 1. 0.3849 0.3869 0.3888 0.3907 0.395 0.3944 0.396 0.3980 0.3997 0.4015 1.3 0.403 0.4049 0.4066 0.408 0.4099 0.4115 0.4131 0.4147 0.416 0.4177 1.4 0.419 0.407 0.4 0.436 0.451 0.465 0.479 0.49 0.4306 0.4319 1.5 0.433 0.4345 0.4357 0.4370 0.438 0.4394 0.4406 0.4418 0.449 0.4441 1.6 0.445 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.455 0.4535 0.4545 1.7 0.4554 0.4564 0.4573 0.458 0.4591 0.4599 0.4608 0.4616 0.465 0.4633 1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706 1.9 0.4713 0.4719 0.476 0.473 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767.0 0.477 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.481 0.4817.1 0.481 0.486 0.4830 0.4834 0.4838 0.484 0.4846 0.4850 0.4854 0.4857. 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916.4 0.4918 0.490 0.49 0.495 0.497 0.499 0.4931 0.493 0.4934 0.4936 10/-
[HGT 19] - 10 -.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.495.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.496 0.4963 0.4964.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.497 0.4973 0.4974.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981.9 0.4981 0.498 0.498 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986 3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990 11/-
[HGT 19] - 11 - Jadual t (Studet's t Table) t table with right tail probabilities df\p 0.40 0.5 0.10 0.05 0.05 0.01 0.005 0.0005 1 0.3490 1.000000 3.077684 6.31375 1.7060 31.805 63.65674 636.619 0.88675 0.816497 1.885618.919986 4.3065 6.96456 9.9484 31.5991 3 0.76671 0.76489 1.637744.353363 3.1845 4.54070 5.84091 1.940 4 0.707 0.740697 1.53306.131847.77645 3.74695 4.60409 8.6103 5 0.67181 0.76687 1.475884.015048.57058 3.36493 4.0314 6.8688 6 0.64835 0.717558 1.439756 1.943180.44691 3.1467 3.70743 5.9588 7 0.63167 0.71114 1.41494 1.894579.3646.99795 3.49948 5.4079 8 0.6191 0.706387 1.396815 1.859548.30600.89646 3.35539 5.0413 9 0.60955 0.707 1.38309 1.833113.616.8144 3.4984 4.7809 10 0.60185 0.69981 1.37184 1.81461.814.76377 3.1697 4.5869 11 0.59556 0.697445 1.363430 1.795885.0099.71808 3.10581 4.4370 1 0.59033 0.695483 1.35617 1.7888.17881.68100 3.05454 4.3178 13 0.58591 0.69389 1.350171 1.770933.16037.65031 3.018 4.08 14 0.5813 0.69417 1.345030 1.761310.14479.6449.97684 4.1405 15 0.57885 0.691197 1.340606 1.753050.13145.6048.94671 4.078 16 0.57599 0.69013 1.336757 1.745884.11991.58349.9078 4.0150 17 0.57347 0.689195 1.333379 1.739607.1098.56693.8983 3.9651 18 0.5713 0.688364 1.330391 1.734064.1009.5538.87844 3.916 19 0.5693 0.68761 1.3778 1.79133.0930.53948.86093 3.8834 0 0.56743 0.686954 1.35341 1.74718.08596.5798.84534 3.8495 1 0.56580 0.68635 1.33188 1.70743.07961.51765.83136 3.8193 0.5643 0.685805 1.3137 1.717144.07387.5083.81876 3.791 3 0.5697 0.685306 1.319460 1.71387.06866.49987.80734 3.7676 1/-
[HGT 19] - 1-4 0.56173 0.684850 1.317836 1.71088.06390.4916.79694 3.7454 5 0.56060 0.684430 1.316345 1.708141.05954.48511.78744 3.751 6 0.55955 0.684043 1.31497 1.705618.05553.47863.77871 3.7066 7 0.55858 0.683685 1.313703 1.70388.05183.4766.77068 3.6896 8 0.55768 0.683353 1.3157 1.701131.04841.46714.7636 3.6739 9 0.55684 0.683044 1.311434 1.69917.0453.460.75639 3.6594 30 0.55605 0.68756 1.310415 1.69761.047.4576.75000 3.6460 if 0.53347 0.674490 1.8155 1.644854 1.95996.3635.57583 3.905 13/-
Jadual Chi Gada dua (Chi-Square Table) Right tail areas for the Chi-square Distributio df\area.995.990.975.950.900.750.500.50.100.050.05.010.005 1 0.00004 0.00016 0.00098 0.00393 0.01579 0.10153 0.45494 1.3330.70554 3.84146 5.0389 6.63490 7.87944 0.01003 0.0010 0.05064 0.1059 0.107 0.57536 1.3869.7759 4.60517 5.99146 7.37776 9.1034 10.59663 3 0.0717 0.11483 0.1580 0.35185 0.58437 1.153.36597 4.10834 6.5139 7.81473 9.34840 11.34487 1.83816 4 0.0699 0.9711 0.4844 0.7107 1.0636 1.956 3.35669 5.3857 7.77944 9.48773 11.1439 13.7670 14.8606 5 0.41174 0.55430 0.8311 1.14548 1.61031.67460 4.35146 6.6568 9.3636 11.07050 1.8350 15.0867 16.74960 6 0.67573 0.8709 1.3734 1.63538.0413 3.45460 5.3481 7.84080 10.64464 1.59159 14.44938 16.81189 18.54758 7 0.9896 1.3904 1.68987.16735.83311 4.5485 6.34581 9.03715 1.01704 14.06714 16.0176 18.47531 0.7774 8 1.34441 1.64650.17973.7364 3.48954 5.07064 7.3441 10.1885 13.36157 15.50731 17.53455 0.0904 1.95495 9 1.73493.08790.70039 3.3511 4.16816 5.89883 8.3483 11.38875 14.68366 16.91898 19.077 1.66599 3.58935 10.15586.5581 3.4697 3.94030 4.86518 6.7370 9.3418 1.54886 15.98718 18.30704 0.48318 3.095 5.18818 11.603 3.05348 3.81575 4.57481 5.57778 7.58414 10.34100 13.70069 17.7501 19.67514 1.9005 4.7497 6.75685 1 3.0738 3.57057 4.40379 5.603 6.30380 8.4384 11.3403 14.84540 18.54935 1.0607 3.33666 6.1697 8.995 13 3.56503 4.1069 5.00875 5.89186 7.04150 9.9907 1.33976 15.98391 19.81193.3603 4.73560 7.6885 9.81947 14 4.07467 4.66043 5.6873 6.57063 7.78953 10.16531 13.3397 17.11693 1.06414 3.68479 6.11895 9.1414 31.31935 15 4.6009 5.935 6.614 7.6094 8.54676 11.03654 14.33886 18.4509.30713 4.99579 7.48839 30.57791 3.8013
16 5.141 5.811 6.90766 7.96165 9.314 11.91 15.33850 19.36886 3.54183 6.963 8.84535 31.99993 34.6719 17 5.697 6.40776 7.56419 8.67176 10.08519 1.79193 16.33818 0.48868 4.76904 7.58711 30.19101 33.40866 35.71847 18 6.6480 7.01491 8.3075 9.39046 10.86494 13.6759 17.33790 1.60489 5.9894 8.86930 31.5638 34.80531 37.15645 19 6.84397 7.6373 8.9065 10.11701 11.65091 14.5600 18.33765.71781 7.0357 30.14353 3.8533 36.19087 38.586 0 7.43384 8.6040 9.59078 10.85081 1.4461 15.45177 19.33743 3.8769 8.41198 31.41043 34.16961 37.5663 39.99685 1 8.03365 8.8970 10.890 11.59131 13.3960 16.34438 0.3373 4.93478 9.61509 3.67057 35.47888 38.9317 41.40106 8.647 9.5449 10.983 1.33801 14.04149 17.396 1.33704 6.0397 30.8138 33.9444 36.78071 40.8936 4.79565 3 9.604 10.1957 11.68855 13.09051 14.84796 18.13730.33688 7.14134 3.00690 35.1746 38.07563 41.63840 44.1818 4 9.8863 10.85636 1.40115 13.84843 15.65868 19.0375 3.33673 8.4115 33.1964 36.41503 39.36408 4.9798 45.55851 5 10.51965 11.5398 13.1197 14.61141 16.47341 19.93934 4.33659 9.33885 34.38159 37.6548 40.64647 44.31410 46.9789 6 11.1604 1.19815 13.84390 15.37916 17.9188 0.84343 5.33646 30.43457 35.56317 38.88514 41.9317 45.64168 48.8988 7 11.80759 1.87850 14.57338 16.15140 18.11390 1.74940 6.33634 31.5841 36.741 40.1137 43.19451 46.9694 49.6449 8 1.46134 13.56471 15.30786 16.9788 18.9394.65716 7.3363 3.6049 37.9159 41.33714 44.46079 48.784 50.99338 9 13.1115 14.5645 16.04707 17.70837 19.76774 3.56659 8.33613 33.71091 39.08747 4.55697 45.79 49.58788 5.3356 30 13.7867 14.95346 16.79077 18.4966 0.5993 4.47761 9.33603 34.79974 40.560 43.7797 46.9794 50.8918 53.67196