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Co e No.: MTE 3105 $r\-ndex No.:

(2 marks)

'\

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Code No.: MTE 3105(b) What is the probability thqt:, ,

(r) the first and second ;rr fr* ffi red ?

(ii) the first candy is brown and the second is red or yeilow?

the second candy is brown given that the first is yeilow?)ivt-_lk {r^; a ',ldk- | ud* * {* fs

(2 marks)

{3 marks}(iii)

L**- 1

(3 marks)

;+

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Code No.: MTE A10S lndex No.:2 (a) l.::Il r:lorred rhat traineEs in a reachers trainino ing instifute watch anverage of 3.0 hours of fyr.dqy. tf the standarO Oeviailon'f, tn.lgtrJ';3;T:*gj- o;;T*"iJ";li T'IJ"T?Jllff#ffiff liisrln*dis'*iffi ";h;;; j,ini,-,1,,i0ffi "il,iiJf T

(1 mark)(it) what is the standard deviation of this sampting distribution?

'.*:.,,' .' s{

(2 marks)-rd

4 4

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(b)MTE 3105 lndex No.:

The masses of 40 men, to the nearest kirogram,:are given as below.74 87 80 71 77 67 80 83 85 7778 84 75 79 73 79 81 77 76 7389 68 74 93 86 65 82 87 80 8378 92 76 78 73 81 75 73 69 78These rnasses are a random sanrple from a population of massesdistributed normally with a var,iance of 40.(i) Give a point estimate for the population mean.

(ii) Find the 95o/o canfidence interval for the(2 marks)

population mean.

(5 marks)5.j

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lndex No.:: :'' -*ii-ir,j;it,lr:p:l sflnpte or lzo.*"oi#k*u,*;ffl* CyTlg the pasr years showed33i,:?i515,ff ilsl**xffi!ffiixffi ,ffi ffi:ff ffi,i[?x?ft :#S?"ffi n:ffi n-,_;*--ffiffimEffi ;,ffi i?JJ:lyJhan 70 years? use a 0.0S brd

(i) , State the nulland

(2 marks)(ii) What is the criticalvalue?

(1 mark)(i'i) Calculate the value of the test statistic.

(3 marks)

6jj

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Code l*o.: MTE 3105

(iv) "_What decision can you rnake b@W, @n (iii)?': ':.., , .'l-;,.1..,.i' . i

. i: : :1''

(v) What conclusion san you

(vi) what is the probability that you have wrongfully rejected the nullhypothesis? :

II--t--1

7,b

Ilnddrt No.::

{1 mark}

(1 mark)

(2 marks)

i/-\-LD

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Gode No.: MTE 3105 lndex No.:

HandphoneModel A B c D ENumber soldduringpromotionalcampaiqn

36 24 34 26 30

Table 1

4' A company specializing in selling handphones recentty taunched a promotionalcampaign in which it offered 5 different-models at a discounted rate.The sales t"n"g", took a randorn semple of 150 sales and collected the set ofdata shown in Table 1.

{}'-t, At q = 0.05, test the hypothesis that there was no preference for differenthandphone models.(i) State the hypotheses for this test.HolHr:

" '.si -: (2 rnarks)(ii) state the degree of freedom and the critical value used in this test.d.f. =

. Critical value =

(2 marks)

I-i.t/

,-

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(iv) What decision can you(4 marks)

(1 mark)

(1 mark)

W,Wsl,{iir)? A(5,

(v) Write a conclusion for the above test.

!i-t -\ril

Ia

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Code No.: MTE 3l0S lndex l,lo.:5' A major distributor of handphgp? wanted to know if consumers are insensitive tolight price changes for a certain,tram# #a.r . The distributor selected fourretail outlets at random to sell that ffi,# of four predetermined prices.After 4 weeks, the number or nanoprron_#=rJiJ'"rcr, week is as ioltows:

545

I1073

3657

4o57

-:-x r=5'5si= t.oz

aS.ZSsl= z-sz

= 7.25= 9.58

= 5.75= 4.92

x42

.91

x3

2Js

Grandtnean, x =5.g37SGrand variance = 4.4625

(a) state the null and alternative hypotheses the distributor will use in anANOVA test. :,__:.

(2 rnarks)

,"a 10

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Code No.: MTE 3105(b) At o= 0.01, test the hypothe@e,ik (*):,(i) State the degree of ftwiffin fur numerator and denominator, hencefind the criticalv*le.

d.t (nunrerator) :*d.f. (denominator) =Critical value = ...

(2 marks)(ii) Evaluate the variansc betweeri groups and the variance withingroups and hence find the F-test value.

( iii) Make a decision about the test above.

(5 rnarksl

(1 mark)

".- 11

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Code No.: MTE 3105

'-w

SECTION B( S0 marks )Answer any TWO questions1' (a) From a large class, four students were chosen randomty and their gradeswere as follows : 64, 66, 89 and 77. The grades for tfre'wrrote class wereassumed to be normally distributed.

.(i) Find a point estimate each of the mean mark and the standarddeviation of the marks of the class.(ii) Find a g5 o/o confidence interval for the mean mark of the class.(iiD With what degree of confidence can it be said that " the mean markof the class is T4 t 9.4 ?(16 marks)

(b)

w

A survey was conducted to estimate the mean annual food expenditure ofhouseholds in Malaysia. From an earlier stuJy,iiwas known that thepopulation standard deviation of the food expenoitrr" *"s RM 1 1 g00.(i) lf the mean anntlllfood expenditure of a random sample of 100househoft^ts was RM20 000; fin-d q gg"/" c.a$iJence.interualforthe mean food expenditure or the nouienoill in Maiiysia ?(ii) How large a sample should be selected so that ilre estii"nate witha 99% confidence level is wiflrin RMB00 of the population mean?(9 rn,arks)

.- 1.2

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(a) A survey of credit card holders revealed the following information asshown in Table 2:

ffry ry *f#*a.b-uf, rabre 2JaP -f +*^rte* A" ,**au,rSTe'st'at the 1% significance levelthat the mean credit balances for allcredit card horders in 19gg and 2000 were different.(10 marks)

A comm-on]y prescribed drug for relieving nervous tension is betieved tobe only 65% effective. . Experimental res-ults show that 82 received reliefwith a new drug administered to a random sample of 110 adults who weresuffering from nervous tension. ls this sufricienluuid*n"" to conclude thatthe n-ew drug is superior to the one commonty pr-es.rihed? Use a 0.05significance level.

(5 marks)A lecturer claims that the exam ma.rks of a pa.ticular group is normallydistributed with mean 63 and standard deviation 7. drando, "urfre ofthe marks of 30 students from the group yietoeo ",r"rn of 6s ancl astandard deviation of B. Test, using o = b.05 to Jetermine whether thetrue standard deviation differs froil. -- -:-

zta) z >g*#*{3-*)f,-,.^.^ .. -s " -:tomarks)

Code No.: MTE 3105

(b)

(c)

Average credit card belenceSize of random samplePopulation standard deviation

RM 4200500

RM 680

RM 3800460

RM 610

.1 13

=7-6 r -

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Code No.: MTE 3105(a) A public opinion pofl surveyed a random sample of 1000 home televisionviewers. Respondents were classified by gender (male or female) and byviewing preference (wl, TV3 or NTV7). Resurts are shown in Table 3below.

Gender TV1 TV3 NTVTMale 200 150 50

Female 250 300 50

Table 3

Do the men's viewing preferences differ significantly from the women'spreferences? Test the above hypothesis at the 5% significance level.

(10 marks)

A group of medical researchers condudted a pilot stiidy to determinewlrether there was a relationship between a person's weight and heartdisease. They did the study with a random sample of 100 patients in alocal hospital.The data collected was shown in Table 4:

Table 4At o-=-0-01-test whether there was-a rela-tionship between a personrs -weight and heart disease.

(b)

AL,Patient'sConditio-n Weight Status

Underweight Normal OverweightHeart disease 3 2 2BNone 17 35 15

,.3 74(15 marks)

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Code No.: MTE 3i0S4' Mr' lrwan, a.plantation superuisor is inveetigatirig the relationship between thedensitv at which a crop is planted and tfre duariti or tne FrJ;;i:"Th;';"t" i, '-. shown in Table 5.

*

(a)Tafte 5(i) Draw a scatter plot for the data in Table S.(ii) Hence describe the relationship between X and y.

:

Find the equation of the regression line of y on X .

When the seed per acre is 150, what is the ie6iEual?*'

- (b)(7 marks)

(8 marks)

(6 marks)

(4 marks)

(c) obtain from your graph, the values of y at X = 145 and X = 1g0.Comment on the accuracy of the values you get. 0

' .u/

(d)

@ Government of Malaysia 2009

-b 15