UNIVERSITI SAINS MALAYSIA

Peperiksaan Semester PertamaSidang Akademik 2003/2004

September/Oktober 2003

BOI 109/4 - Biostatistik

Masa : [3 jam]

Sila pastikan bahawa kertas peperiksaan ini menganclungi LIMABELAS muka surat yang bercetak (termasuk SEPULUH muka suratformula clan jaclual) sebelum anda memulakan peperiksaan ini .

Jawab LIMA daripada ENAM soalan yang diberikan, dalam BahasaMalaysia .

Tiap-tiap soalan bernilai 20 markah .

Guna kaedah nonparametrik hanya jika kaedah parametrik tidak bolehcligunakan

[BOI 10914]

1 . Untuk mengkaji tahap pencemaran udara di sesuatu kawasanperindustrian bahan pencemar yang sering dimantau ialah nitrogen oksidadan hidrokarbon . Kandungan bahan pencemar ini telah ditentukan di 12lokasi di kawasan perindustrian Prai . Nilai-nilainya (dalam unit

g /m3)adalah seperti berikut :

Berasaskan data ini bolehkah kita mengatakan bahawa kandungannitrogen oksida dan hidrokarbon di kawasan berkenaan sama?

(10 markah)

Anda telah diberitahu bahawa min kandungan hidrokarbon dikawasan berkenaan bagi 15 tahun terdahulu ialah 75 g/m3 .Berasaskan maklumat-maklumat ini, apa yang dapat andasimpulkan mengenai keadaan udara di kawasan perindustrian Praiketika ini .

(10 markah)

Lokasi Nitrogen oksida Hidrokarbon1 91 952 116 1183 104 1084 84 895 77 716 61 667 84 838 81 889 72 7610 61 6811 97 9612 84 81

[BOI 10914]

2 . Bagi kedua-dua kes di bawah, huraikan bagaimana anda akanmenjalankan kajian berkenaan dan seterusnya huraikan juga kaedahstatistik yang sesuai bagi menganalisis data yang akan dihasilkan . Bagipenghuraian statistik, sertakan hipotesis, ujian statistik, nilai genting(kawasan tolak) dan kesimpulan jika Ho ditolak .

Anda diberi anak Wan siakap dan diminta mengkaji kesan saliniti airlaut terhadap pembesaran anak ikan ini . Saliniti yang perlu dikajiialah 10 dan 30 %o.

(10 markah)

(b)

Anda diberi rambutan yang telah diperolehi daripada 2 pembekal.Anda diminta menentukan rambutan yang mana yang lebih sedap.

(10 markah)

3.

(a) Apakah yang dimaksudkan dengan kuasa bagi sesuatu ujianstatistik itu?

(5 markah)

(b)

Karbon dioksida (C02 ) diketahui mempengaruhi kadar pembesaranmikrob . Di dalam suatu eksperimen kadar pembesaran sejenismikrob Pseudomonas fragi telah ditentukan pada 2 araskandungan C02. Hasil yang dicerap ialah peratus perubahan jisimsel selepas tempoh 1 jam . Data yang diperolehi adalah sepertiberikut :

Adakah terdapat bukti yang cukup daripada data ini untuk kitamengatakan bahawa kandungan C02 yang tinggi merencat(mengurangkan) kadar pembesaran organisma tersebut?

(15 markah)

Aras COZ Peratus erubahan jisim selRendah 62.6 59.6 64 .5 59.3 58.6 64 .6 50 .9 56 .2 52.3 62 .8

44.3 47 .5 49.5 48.5 50 .4 35.2 49 .9 42.6 41 .6

[BOI 109/4]

4.

Satu kajian tentang kandungan protein di dalam hati Ran kelisa telahdijalankan di mana hati Ran tersebut telah diolah dengan 3 jenis sebatianaromatik untuk mengetahui sama ada kandungan protein berbeza antaraolahan. Lima ekor ikan kelisa jantan yang sebaya (sama umur) dipilihsecara rawak untuk clijaclikan sebagai faktor blok bagi struktureksperimen ini . Tiga spesimen tisu hati (bersaiz sama) telah diambildaripada setiap ekor ikan tadi . Kandungan protein (dalam unit mg/g) bagisetiap spesimen clitentukan clan hasilnya adalah seperti berikut :

Uji hipotesis yang mengatakan tiada perbezaan kandungan protein dalam tisuhati ikan yang diolah dengan 3 jenis sebatian aromatik ini .

(20 markah)

5.

Suatu eksperimen telah direkabentuk untuk mengkaji tempoh membekubagi plasma darah daripada peserta yang menghiclap penyakit clarahbeku . Lima kepekatan sampel plasma yang diperolehi secara rawakdaripada pesakit telah disediakan . Tempoh membeku setiap sampeladalah seperti berikut:

Kepekatan (%)

0.01

0.1

1.0

10.0

100[ Tempoh membeku (saat)

95

82

71

58

52

(a)

Adakah terclapat pertalian linear antara dua parameter ini? Jikaada, tunjukkan pertalian tersebut dalam suatu persarnaan clannyatakan berapa kuatkah pertalian tersebut .

(15 markah)

(b) Jika anda menyediakan plasma dengan kepekatan 0.001%,apakah anggaran tempoh bekunya? Bolehkah anggaran inidianggap baik?

(5 markah)

Sebatian AromatikIkan phenanthrene fluoranthene naphthalene

1 9.1 14.4 12.72 13.0 12 .8 20.53 15.7 13 .4 11 .34 10.4 4.1 9.15 9.5 20 .3 18.5

6.

Kandungan kadmium (Cd) bagi 4 spesies rumpai laut telah ditentukandengan menggunakan 5 sampel bagi setiap spesies. Spesies-spesiestersebut ialah Pelvetia sp., Fucus vasiculosus, Ascophyllum sp., danLaminaria sp. Berasaskan maklumat-maklumat berikut, beri kesimpulanmengenai aras pencemaran Cd bagi 4 spesies rumpai laut ini .

Nilai-nilai ANOVA:

TSS = 0. 1806

SSB = 0.1162

- 000 O 000 -

[BOI 109/4]

(20 markah)

Spesies Pelvetia sp. F. vasiculosus Ascophyllum Laminaria sp.sp .

Min 2.01 2.15 2 .05 1 .94kandunganCd (mg/g)

FORMULAYANG MUNGKIN DIPERLUKAN

YA. z

- uo

B . t =

(Yt - Y2)s4(1/n,)

+ (1/n2)

C. t

F s

H. X2 =

J . S2 =

Of

2. C = 1 -

(Yi - Y2)(S2,,/n,) + (s2/n2 )

D. z = Y - 0.570.257

-

I(n, -1)si

+

(n2 -1) s2n,+n2 -2

G.

~ t' I

_

(t,siln, )

+

(t2s2/n2)(Si/n,) + (s2ln2)

E(ni,-

Ei1)2

Eii

_1 xd2 _ (Edi)2

n-1 1 i

n

K.

Ujian statistik Kruskal - Wallis

1 .

H

=

N(N + 1)

I-'2

-

3 (N + 1)i ., i

ETN3 - N

3 . E'T = E(t3 - ti)

ik Frledman

12 aba (a + 1)

Ri - 3b (a+ 1)i=1

ik Wilcoxon

n4 1

n(n + 1)(2n + 1)24

- g.T

CYT

ik Mann - Whitney

n n

+ ni (nt + 1)

Ri 2

2

- i

nine - U

O.

Ujian Blok Rawak:

1 .

TSS =

Y~ -n2

Tit G22 .

SST = ~b -

3 . SSB =

BOI 109/4

L. Ujian stadst2

1 . Xt -

M. Ujian statis

1 . 9T =

2. aT =

3 . Z =

N . Ujian statis

1 . U =

2. U' =

P.

Ujian Segiernpat sarna Latin

22 .

SSR = E R~-n

3 .

SSC = Ii - n2

Q.

Eksperimen Faktoran

1 . SSA =~n n2 - 2

2 22. SSB = E

B -

(AB)~

G23 .

1E

nAB

SSA - SSB -

= SSABAB

nR .

Ujian Sepenuh rawak:

1 . SSB =

T-ii-e - G2

n

S . Regmsi

SS= YX2 - (EX)2n

r

Ssxv

SSxv=SSxx SSYY

SSxx

T.

Perbandingan berganda:

G2n

xX lSSxy = Exy -nY

2LSD = t~ ~sW (nl.

+

n.)

Wr = qa (r, v) ~1 Sn

BOI 109/4

Jadual 1: Keluasan Lengkung Normal

BOI 109/4

This table is abridged from Table i of Statistical Tables and Formulas, by A. Hald(New York : John Wiley & Sons, IM). Reproduced b~ permission of A . Haid and thepublishers; John Wiley & Sons.

z .00 .01 .02 .03 .04 .05 -.06 .07 .08 .090.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .03590.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .07530.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .11410.3 .1179 x;1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .15170.4 .1554 O S91S91 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .18790.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .22240.6 \ .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .25490.7 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 - .2823 .28520,8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .31330.9 , 3159 .3186 .3212 .3238 .3264 .3289 :3315 .3340 .3365 .33891.0 13413 .3438 .3461 .3485 .5508 .3531 .3554 .3577 .3599 .36211 .1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .38301 .2 .3849 .3869 .3888 .3907 - .392S .3944 .3962 .3980 .399.7 .40151 .3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177I .4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .43191 .5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .44411.6 .4452 .4463 .4474 .4484 ,.4495 .4505 .4515 .4525 .4535. .45451.7 .4554 .4564 .4573 .4582'.4591 .4599 .4608 .4616 .4625 .46331.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .47061 .9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .47672.0 .4772 .4778 .4783 .4788 .4793 .4798 :4863 '.4808 .4812 .48172.1 .4821 .4826 A830 .4834 .4838 .4842 .4846 .4850 .4854 .48572.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .48902.3 .4893 .4896 .4898 .4901 .4904 . .4906 .4909 .4911 .4913 .49162.4 .4918 .4920. .4922 .4925 .4927 .4929 .4931 .4932 .4934 .49362.5 .4938 .4940 A941 .4943 .4945 .4946 .4948 .4949 .4951 .49522.6 .4953 .4955 .4956 :4957 .4959 .4960 .4961 .4962 .4963 .49642.7 .4965 .4966 .4967 A969' .4969 .4970 .4971 .4972 .4973 .49742.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .49812.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .49863.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990

Jadual 2: Titik Peratusan Taburan t

- 10 -

From "Table of Percentage Points of the t-distribution." Computed byMaxine Merrington, Biometrika, Vol . 32 (1941), p . 300. Reproduced bypermission of the Biometrika Trustees. '

.'

BO.I 109/4

df a= .10 a= .05 a- .025 a- .010 a= .005

1 3.078 ' 6.314 12.706 31.821 63.6572 1.886 2.920 4.303, 6.965 9.9253 1.638 2.353 3.182 4.541 - 5.8414 1.533 2.132 2.776 3.747 4.604

5 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.7077 1.415 1 .895 2.365 2.998 3.4998 1.397 1.860 . 2.306 2.896 3.3559 x.383 1.833 2.262 2.821 . 3.250

10 1 .372 11:812 2.228 2.764 3.16911 1 .363 1 .796 2.201 2.718 ' 3.10612 1 .356 1.782 2.179 2.681 3.05513 1.350 1 .771 2.160 2.650 3.01214 1.345 1 .761 2.145 2.624 2.97715 1.341 1 .753 2.131 ' 2.602 2.947

16 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1 .734 2.101 2.552 2.87819 1.328 1 .729 2:093 2.539 2.861

.20 1.3,25 1 .725 2.086 2.528 2.845

21 1.323 1 .721 2.080 2.518 2.83122 1 .321 1.717 2.074 2.508 2.81923 1 .319 1.714 2.069 2.500 2.80724 1 .318 1 .711 2.064 2.492 2.79725 1.316 1 .708 2.060 2.485 2.787

26 1.315 1 .706 2.056 2.479 2.77927 1.314 1.703 2.052 2.473 2.77128 1.313 1.701 2.048 2.467 2.76329 1 .311 1.699 2.045 2.462 2.756inf. 1 .282 1 .645' 1 .960 - 2.326 2.576

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0. O O O ~+ - N Nen C+iC1u9CIV" tel .ei tC nNO?'DCn- C N

mml"nOCDof ben-o1n

dUiV`tn)._ )n-Ii -O1n cc O1 O -. CM b t0 ri m td 4 Oi G Oi n" - "" ---- -- -- -NMV " to to'

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'...n CM O1.N, M m 1n M CIp1cn-nC1d.Nen nn n

~p-~+IDmnt~j mOMfMto .r no)Mo1-~ 00-V" I-

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. -~mtnHM0 C,nVM" C+M1Vm"

tONtD0)r- M ton-ttooN.ro 000.C . :C'~ ."NN 0itai4uiMi e0cGtzmC aiOC'"-" C4.~ .~ _ .-. . ..citaidycC toV~tri.~NM~ tXi hV'In br.

ell_pm OVm",n

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MV.O,Ng g N-bl OOft~

nVN-O -'bcp inH %IMtnMnm0 m ~00qN=O1N In1~M

In mNtDOm, inCnOtn-IDYlnOtD N "~NWM!n at V" tTtnNmN--+m NOm1nbNV"

to-mtnNV. cpK)b000 d " ehvlS

OCOO CO-%~N Ndftald "t totlfcpnn epeppiCO -~NCYaf~ O -n~FNMn

tnnNMNN an V " Oh to 91

en -C4

MC O_$ IC41 110, '"o n CO 40 %D N C4 cm

A OtONn0 _f-SV.VM"e.4Dmttnn "tHOr,tD-tDOtnO 8VN" O11~DVM" MM VN" tODObD " ~t0D0I"O= Ob0pO1 nnObfNb OOOO COC-+ "-. NNM0)V"b-IDNCOW; to %D to

V " OIDCNCOr.CO00atC%

tn_RV "O--~eiC Ine.0+tn.

aiO~viN " -Mai ainN NM V" to Y') t0

NC,V. tn4Dr.0001 -O .~-N.=~ ^t~nm~ " NNNNC~V NQb"CNAM " 0 " .n33 -00000018C4 en

BOI 109/4

Jadual 5: Titik Peratusan bagi Ujian Julat Berganda Baeu Duncan

RWmd-4UoaOJ.OwaM.WI14YRAWrWA*kiTtsn.fla~weuis,11 : 5-42,19SS. S7kh Pa=le ks Iron Me 4:...uk Sodep rd yes~otlw.

Enw' r "aadaofadrirditembell-wry

4f a 2 3 4 S 6 7 .8 9 70 12 14 16 !d 20

1 AS 1L0 ILO lu 18 .0 16:0 18.0 ILO ILO ILO ILO ILO lu ILO 18 .0At 90.0 90A 90.0 90.0 90A 90.0 90.0 90.0 90 .0 90A 90.0 90.0 90.0 90.0

2 AS L09 6A9 L09 6.0! 60 609 6,09 6.09 6.09 6A9 6A9 6.09 6.09 6A9A1 14A 14:0 14A 14A 14LO 14A 14.0 14.0 14.0 14A 14.0 14 .0 14.0 14.0

3 AS 430 430 4.50 4.50 4.50 430 430 4.50 4.SO 430 4.50 4.50 4.50 4.50A1 L26 LS L6 L7 L8' L9 L9 9.0 9.0 9.0 9.1 9.2 9.3 9.3

4 AS 393 4.01 4.02 4.02 4.02 4.02 4.02 4.02 4.02 4.02 4.02 4.02 4.02 4.02A1 6.51 6J 69 7.0 7.1 7.1 7.2 7.2 73 7.3 7.4 7.4 7.5 7.S

S AS 3.64 3.74 3.79 183 3.93 3.83 3.83 3.83 183 3.93 3.83 3.63 3.83 3.83A1 5.70 S.96 6.11 6.18 6.26 633 6.40 6.44 6.S 6.6 6.6 6.7 6.7 6.8

6 AS 3.46 338 3.64 3.68 3.68 3.68 3.68 3.68 3.66 3.66 3.68 3.68 3.68 3.66A1 524 S.SI S.6S 5.73 S.81 3.61 S9S 6A0 6A 6.1 6.2 6.2 6.3 6.3

7 AS 333 3.47 ,334 338 3.60 3.61 3.61 3.61 3.61 3.61 3.61 3.61 3.61 3.61A1 4.9; S22 S37 US SM 5.61 S.69 5.73 S.8 S.8 S.9 S.9 6.0 6.0

8 A3 3.26 339 3.47 332 33S 3.S6 3.S6 . 336 336 3.56 3.S6 336 3.56 3.S6A1 4.74 SAO S.14 S23 S32 5.40 5.47 S.SI `S.S S.6 S.7 5.7 S.9 S3

9 AS 3.20 3.34" 3.41 3.47 3.30 9.52 332 332 3.52 332 3.52 332 3.52 332A1 4.60 4.86 4.99 SAl 5.17 SM S32 S36 S.4 ' S.S S.S S.6 5.7 S .7

10 AS 3.IS 330 337 3.43 3.46 3.47 3.47 3.47 3.47 3.47 3.47 3.47 3.47 3.46Al 4.48 4.73 4.99 4.96 $A6 5:13 S.20 5.24 5.28 5.36 5.42 5.49 S34 S.SS

11 AS 3.11 327 33S 339 3.43 3.44 3.45 3.46 3.46 3.46 3.46 3.46 3.47 3.48A1 439 4.63 477 4,86 4.94 5.01 S.06 5.72 S.IS S24 3.28 5.34 5.38 S.39

12 AS 3.08 3.23 333 336 3A0 3.42 3.44 3.44 3.46 3.46 3.46 3.46 3.47 3.48At 432 4.S3 4.68 4.76 4.84 4.92 4.96 SM 5.07 5.13 S.17 S.22 S.23 5.26

13 AS 3A` 321 3.30 33S 338 3.41 3.42 3A4 145 3.4S 3.46 3.46 3.47 3.47A1 426 4.48 4.62 4.69 4.74 4.84 4.88 4.94 498 5.04 5.06 5.13 S.14 S.15

14 AS 3A3 3.18 3.27 333 337 339 3.41 3A2 3.44 14S 3.46 3.r6 3.47 3.47A1 421 4.42 43S 4.63 4.70 4.78 4.83 4.97 431 -4.96 SAO 5.04 S.06 S.07

IS ,& AS 3A1 3.16 32S 331 336 338 3.40 3.42 3.43 3.44 14S 3.46 3.47 3.47Al '4.T7 437 4,50 438 4.64 4.72 4.fl 4.81 4.84 4.90 4.94 497 4.99 S.00

16 AS 3A0 MS 3.23 330 334 337 339 3.41 3.43 3.44 3.4S 3.46 3.47 3.47A1 4.13 434 44S 434 4.60 4.67 4.72 4.76 4.79 4.84 4.86 491 4.93 4.94

17 AS 298 3.13 322 328 333 336 3.38 3.40 3.42 3.44 3.45 3.46 3.47 3.47.01 4.10 430 4.41 430 436 4.63 4.68 4.72 4.7S 4.80 4.83 4.86 4.86 4.99

18 .OS 297 L12 321 127 332 335 337 339 3.41 3.43 145 3.46 3.47 3.4701 407 427 438 4.46 4.S3 4.59 4.64 4.68 4.71 4.76 4.79 4.82 4.84 4.9S

19 AS 296 3.11 3.19 3.26 3,31 3,33 337, 339 3.41 3.43 3.44 3.46 3.47 3.47A1 US 424 43S 4.43 430 4.56 4.61 4.64 4.67 . 4.72 4.76 4.79 4.61 4.12

20 AS 295 3.10 3.18 325 3.30 334 336 331 3.40 3.43 3.44 3.46 3.46 3.47.01 4.02 4.22 433 4.40 4.47 433 4.58 4.61 4.6S 4.69 4.73 4.76 4.78 4.79

22 AS 293 3A 3.17 3.24 329 - 332 335 337 339 3.42 344 3.4S 3.46 3.47A1 399 4.17 4.28 4.36 4.42 448 433 4.57 4.60 4AS 4.69 4.71 4.74 4.75

24 AS 292 3.07 - MS 322 328 331 3.34 337 338 3.41 3.44 3.45 3.46 3.47A1 396 4.14 ' 424 433 439 4.44 4.49 4.53 437 4.62 4.64 4.67 4.70 4.72

26 .05 291 3.06 114 321 127 3.30 3.34 3.36 338 3.41 3.43 3.45 3.46 3.47A1 393 4.11 421 430 436 4.41 4.46 4.30 433 439 4.62 4.65 ' 4.67 4.69

29 AS 2.90 344 3.13 320. 326 330 333 335 3.37 3.40 3.43 MS 3.46 3.47A1 391 348 4.18 4.28 434 439 4.43 4.47 431 436 4.60 4.62 4.6S 4.67

30 AS 2.89 3.04 '3.12 120 32S 3.29 332 33S 337 3.40 143 3.44 3.46 3.47AI 3.89 4.06 4.16 422 432 436 4.41 4.45 4.49 4.54 4.56 4.61 4.63 4.65

40 AS 2.86 3.01 3.10 3.17 322 327 330 333 33S 339 3.42 3.44 3.46 3.47At 3.12 3.99 410 417 .424 4.30 4.34 437 441 4.46 4.S1 4.54 4.S7 4.S9

60 AS 2.83 239 3A8 3.14 32D 324 3.29 331 333 337 3.40 3.43 3.4S 3.47Al 3.76 3.92 4A3 412 4.17 423 427 431 434 439 444 4.47 4.50 4.S3

100 AS 2.90 2.93 3.05 112 3.19 3.22 326 3.29 332 3.36 3.40 3.42 MS 3.47A1 3.71 3.86 393 406 411 4.17 4.21 42S 4.29 43S 439 4.42 4.4S 4.49

t. AS 2.77 2.92 SA2 30 3.15 3.19 3.23 3.26 3.29 334 338 3.41 3.44 3.47Al 3.64 180 330 1" 444 4.09 4.14 417 420 426 4.31 434 4.38 4.41

Jadual 6 : Nilai Genting bagi Ujian Pangkat Bertanda Wilcoxon

- 14 -

One-sided Two-Sided n=5

.05 .10 1

.025 .OS.01 .02.005 .01

n=17

13011770292

FromSome RapidApproxlraatcStatiidWProcedurO (Revised) by Frank Wilcoxon and Roberta A. Wilcox (Purl River . N.Y .: Lederle Laboratories.1%4) . Table 2. Reproduced by permiuion Of Ledede Laboratories. a wonof American Cyanamid Company.

.025

.01

.005

.05.02.01

352823

n=29

47403328

n=30

54463832_

n=31

60524337

n=32

68594943 .

n=33

75665649

n=34

83736255

n=35

92816961

n=36

101907768

n=37

110988576

n=38

1201079384

n=39.05 .10 141 152 163 ' 175 188 201 214 228 242 256 271.025 .OS 127 137 148 159 171 183 195 208 222 23S 250.01 _02 111 120 130 141 157 162 174 186 198 211 224.005 .01 IOQ 109 118 128 138 149 160 171 183 195 208

n=40 n=41 n=42 n=43 n=44 n=45 n=46 n=47 n=48 n=49 n=50.05 .10 287 303 319 336 353 371 389 408 427 446 466.025 .05 264 279 295 311 327 344 361 379 397 415 434.01 .02 - 238 252 267 281 297 313 329 345 362 380 398.005 .01 221 234 248 262 277 292 307 323 339 356 373

t+ = S(1)SO

n=6 n=7 n=8 n=9 a=10 n=11 n=12 n=13 n=14 n=15 n=16

2 4 6 8 11 14 - 17 21 26 30 361 2 4 6 8 11 14 17 21 25 300 2 3 5 7 10 13 16 20 240 2 3 5 7 10 13 16 19

n=18 n=19 n=20 n=21 n=22 n=23 a=24 rn=25 n=26 n=27 n=28

Jadual 7: Nilai Genting Taburan U Mann-Whitney

:C2) : 0,20 0,10 O .Cs 0 .02 O.Q1 O.F.0S 0 .002 .0.0.01

nl

at

aCI) :n2 1

3t 139 140 1

0 .10

192203202

0.05

210215221

4.us

220226232

0 .c.1

232232244

0.005

240266232

4.0425

2472S3259

4.001 0.oo0S

_____________2SS 260261 - 267262 273

__------}------------------ -----------» __----------9 9 1 56 60 64 67 70 72 74 76

10 1 62 66 70 74 77 79 92 23

it 1 62 72 76 91 23 26 i9 9112 1 73 7t t2 27 90 93 96 9233 1 79 214 t9 94 97 300 103 106114 1 25 90 95 140 204, 107 lit 11315 l 90 96 1.01 107 111 214 112 120

is 1 96 102 107 11s 227 121 12S 12217 1 101 302 Ilk 120 124 222 132 13528 1 107 114 120 126 131 13S -139 14219 1 113 120 126 133 132 1%2 346 ISO20 1 112 126 132 140 11414 lag 1S4 157

21 1 126 132 239 166 131 is$ 161 16422 1 230 132 1145 153 152 162 162 17223 1 235 1144 151 139 164 169 27S 17924 1 161 150 . 157 166 171 176 122 12625 1 347 156 163 172 171 123 129 193

26 1 152 162 270 179 115 290 196 20127 1 Is$ 162 176 its 191 197 203 20221 1 164 1714 212 192 292 204 211 21S29 1 169 179 122 191 20S 211 212 22230 ( 175 125 1914 205 212 212 22S 230

33 1 1(0 191 231 211 211 211.6 232 23732 1 11;6 297 207 211 225 231 239 24433 1 192 203 213 224 232 232 246 2S134 1 197 209 219 231 232 263 2S3 2S935 1 203 22S 226 237 2145 2S2 260 266

36 1 209 221 _32 2LL 732 2S9 267 27337 1 216 227 231 2S0 231 256 275 22031 1 220 233 244 257 265 273 222 22139 1 22S 239 250 263 272 220 229 29S

9 40 1 231 245 257 270 2733 226 296 502------------M-____~ __ _~-------------___ __ »__-_____10 30 1 62 73 77 21 24 27 90 92

11 1 74 79 24 22 92 94 92 10012 1 11 $6 92 96 99 102 106 lot13 1 27 93 S7 103 lof 110 113 11626 1 93 99 2014 110 114 117 121 12415 1 99 106 111 127 121 125 229 132

16 1 106 112 1111 ' 124 225 133 137 114017 1 112 119 12S 132 136 140 24S 142is 1 111 125 132 139 243 249 1ST 15629 ( 121, 132 132 146 IS2 355 161 16420 1 130 IM its 153 132 163 162 172

20 21 1 137 1145 152 160 266 170 276 290