Tll

l

(b) There are 78 tennis players in a competition.about them.

$€GX NO.:

[2 marksJ

Table 1 gives detail information

56 school-levelPlaYers

29 rnale 7left-handed-27 female 3left-handed

22 state-levelplayers

12 male 6left-handed10 female 2-left,handed;.

Table I(i) Find the probability that a female player selected at random is left-handed.

[2 marksJ

(ii) Find the probability that a iight-hanoed male player selected at random isa school-levelplayer.

{'!

t.\J

_".ia

-'..:&..-*-," !

[2 marks]

2.

SOBE: *frT€3105 ft@€x f*o.:

According to a report by ttre €€ffig,ffi,Ao"tg$qtiqn of penang, the average}early households income of Pe*rang ww RM15,SZB h ZOOZ U"r.O bn a randornsample of 40o housGhdds. Fm.@;@- sre average yearly householdsincome of Penangwas RM16,000 ffid tfie etwrdard deviation was RM42ffi..

(a) (i) what is the mean h# $andard deviation of the samplingdistribution of the rnean incomes for all samples

.of 400

hotiseholds ?

13 marksl

what is the probability that the mean income of a random sample of400 households is greater than RM16,000 ?

.j

{L

(ii)

v

4

[2 marks]

lil{ffiffix No.:

: .,: i^i., .:. .j: : ,

tr) |1l . ,*r:u.: :n"f

con{idenee inryry fur,*rc ?:qs7 mean rncorre for ail; :

thre hciuseholds in Penang. ,. :

--r,r j t -., ,',",, i-..-;:';l'r':i ''"r "

' : i '

G

ti.v

(ii) Suggest two ways of improving

9,!.

(

[3;marks ]. : :.

the confidence inter.val in (i)

.3

[2 marks]

I-I

I

ffi8$:t*TEs*S

3 {e} A oports u& W ffi" r'

1pG*8*F Srw$'si ef 'm'diffi40.8 mi$#item ,per *@@*v6rage of all ael$e b Sg,.F

writer's claim at cr,=0.05'?

*f,t5,$ggq @, * ruw* ef'&v}&iSSru#kg. F&

sw&rs*belw@.ffiriffis

[6 marks J

at,.

6,,t

.t

:6-:ti i ';J..t i:,11

., -.F- ::i _1: r: i r

Fqpuletisn Set you have

fl mark l

(ii) Basgd on the conetiiffiri dil:yorli test, is there a possibility that the

athleles' maxlrnaloryEm,' is not different from the average of

all adults ? Why is S,@ €trGf{ a possibility ?, ,: , .-,!, {,:ri *t:l }.:.:tli ::,: ,,',: . , :

-i. rl,, _i l

'-{/

(ii i) What is the probability that

hypothesis ? ' o

you have wrongfully

[2 marksl

rejected the null t

s_'

7;.

*j*ls-.,--

.l [1 mark ]

CODE: [ilTE31sg s*tlEX i,to.:

t..

Gender Two-n*raeldrive

Four-wheeldrive

Total

Male 23 43 oo

Female 1B 6 24

Total 41 49 90

Table 2

At a = 0.05, test the hypothesis that the vehicle preference is independent ofgender.

(a) What are the hypotheses?

4. A study was con&rted to debrrnine sfr#sr,Sle pre&rence for a two_wheeldrive or a four-wheeldrive veh*# l#b &b gender of tr€ purchaser Asample of 90 buyers was selecsd, W ne deta are shown in tiOte Z.

(2 marks)

'8

.ir

tr)(')

Complete the table below.

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Observationfrequency

(o)

Expected'frequency

(E)

L,i1 -':i: l':

(o€) (o-E)'

(o- E'E

23

43

18

6

.a

(5 marks)

Itrli.

I

cs-oe MTE3ros

(ii) Find the crjticat vdue.

(iii) Decide tr H"' could be refie@d:

(iv) Make a conclusion based on (iii).

S@EX HO.:

; i.'i' _*__1''r "j ' l

(1 mark)

(1 rnark)

-.-

x0

@xNO.:

A researcher wishes to see wli@&ry:k py difference in the weightgains of three speciat diets. ffit**r *m,.,+gffi"irlg*o to three groupsand placed on the diet for four weere. Th;i4higJ", (in pounds) areshown here. At a _= 0-01, car fuwc*rer;nErud" that there is adifference in the diets?

I

3

3

6

7

4

10

12

11 2

14s

i,=5

5f = 3.33

11.25

sr= s'zs

", = a.S

t

5, = 7'oo

x2=

Grand.mean, x = 7.08

Grand variance = 15.54

t\-$./ (a) State the hypotheses.

..i3

11

(2 marks)

CSDE: MTE3105

..ij

s&EX,H0":

'tr) $ Find the crtffed vahra.

(iD Compute the F-test value.

(iii) What conclusion can you make?

Fi

:I

(2 marks)

(5 marks)

12

(1 mark)

GODE: MTE310S. INDEX NO.:

SECTION B

(50 Marks)

AnsweranytwoquestionsfromthissectionintheanSWersheetsprovided.

1(a) A college decided to introduce a new Physical Education programme for all the442Year 1 students to improve their fitn"ss. ln order to see whether theprogramme was effective, several tests were done. For one of these, thestudents were timed on a run of 1 kilometer in their first week in the college andagain 10 weeks later. A random sample of 100 students did both runs. Thedifferences of their mean times in both runs were calculated. in" p"prr"ii".mean and standard deviation were found to be 0.75 minutes and 1.62 minutesrespectively.

Assume that the differences are distributed hormally, calculate a g1o/o confidenceinterval for the population mean difference.

Based on your calculations, justify your conclusion whether the new prograrnmehad led to an improvement of at reait 30 seconds_11 $e3ver"gu iir"rz

[10 Marks]

Ahmad's father has a large number of rambutan trees, all of the same variety andage' Ahmad wants to eslimate the mean yield of his father's trees. He collectedall the rambutan from 8 trees and recorded the tottowin'g *"ight, i" il"";;;;kilogram.

JB

(b)

36 53 7767 92 59 ob

(i)

(i i)

( iii)

(iv)

Explain briefly how Ahmad should select a sample of B trees from thosegrowing in the orchard to estimate the mean yield of the rambutan truur.

Find the point estimate for the mean and standard deviation of the yields.

construct a g5% confidence intervar for the mean yierd.fi

state the statistical assumption required for,procedure in (iii) to be valid.

1

13

[15 Marks]

r

{t,

CODE: MTE310S INDEX NO.:

2(a) (i) state the five procedure steps fortesting.hypotheses.

. (5 marks)

(ii) A teacher wishes to know if the variance in scores of the 23 trainees in hisclass is greater than the varipnce of the population. The varianbe of the.class is 198. ls there enough evidence toiupport the ctaim that thevariation of the student is greater than the population variance (o2 = 22Slat a = 0.01?

(10 marks)

(b) From the test result, the teacher claims that at leastll%of the population scoresmore than 70 marks- To see if his claim is valid, the teacher selected a sample of g0students and found that 55 of them score more than 70 marks. At a = 0.01, can it beconcluded that at leastrTo/o of the population score more than 70 marks?

(10 marks)

'..,..-. '".. '....'. . *;;3(a) A medical officer from Hospital Melaka hypothesized that the distribution of bloodphenotypes are as shown in Table 4 below.

Ltv.

Table 4

A. random sample oi zoo individuals was selected and their recorded bloodphenotypes are as shown in Table 5.

,. Table S't

At the 0'01 level of significance, test whether there is sufficient evidence to showthat the hypothesized distribution is incorrect.

Blood T A B AB oNumber 89 18 12 B1

14

[15 marksJ

CODE: MTE3105 INDEX NO.:

Table 6

At q = 0'05, can the sociologist conclude that the years of college education aredependent on the person's location?

[10 marks]

Dr' Maria wants io determine the retation between age and blood pressure of herpatients. The data of her study are shown in Table 7.

43 4B 56 61 67 70H 128 -120 135* 1'43 141 152

Table 7

(a) Plot the data in Table 7 on a scatter diagram.

\ 15 marksl(b) (') ' Find the equation of regression line.(ii) lnterpret the values of siope and y-intercept for the answer in (b) (i).

[10 marks]

Estimate the value of blood pressure when the age is:

(il 46 years old, and(ii) 85 years otd.

Comment on likely the accuracy of your predictions.tI

When the aEe is 56 years old, what is the residual.

A sociologist wishes to see whether the number of years of college a person hascoinpleted is related jo h\ or her prace of resioenfe. A sampre of r1peopre isselected and classified as shown in Table 6.

F..i.9

4.

iit-..Y.

.t

(d)

[8 marks]

@ Government of Malaysia 2010

%. EducationNo

12 8E 15 ,96 I T

,Age, x (yqars)

El-octplg$grgJ

'j

15

[2 marks]