group 22 assignment 7 draft

8/18/2019 Group 22 Assignment 7 Draft

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1ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

Assignment 7: Statistics

Group 22 Members:

Benedicto Munthali

Roelof Jacobs

Kevin olmin!

"holl# e$i

John Ro%burgh &"'(

)ord *ount)ords +"ables ,igures -./

"otal + 6446

Abstract

"his report loo!s at four different case studies to demonstrate different

statistical anal#sis functions0 "he follo1ing statistical concepts are

investigated0 ormal distribution3 stastistical difference from a mean3

significance of difference bet1een a set of t1o results3 reproducibilit#3

repeatabilit#3 and correlation bet1een dependent results0 4t also e%plores

errors and measurement uncertainties0 Results are related to 1hat could be

e%pected from concrete0

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Group Assignment 7 Statistics

-0 "he concrete for the central core of a high+rise building is re5uired to have a

modulus of elasticit#3 63 of / G8A for deflection control0 "he concrete supplier

has carried out a series of tests on successive batches of a potential concrete andobtained the follo1ing values for 6:

-0/3 /0/3 903 90;3 2073 -03 -0;3 -03 /03 9iscuss an# action that #ou could ta!e if #ou 1ere the technical manager 1ith

responsibilit# for these t1o plants0

"able -

90 @ou have been as!ed to evaluate the performance of t1o laboratories in

measuring the properties of 8ortland cement0 "o assist #ou in this3 #ou have

as!ed each laborator# to carr# out repeat tests &to BS 6 -;+-( on cement

samples ta!en from a single batch of cement0 "he values of initial set and 2< da#

compressive strength obtained b# each laborator# are given in table 20

)hat conclusions can #ou dra1 from these results=

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2< da# concrete strengths&M8a(

batch no plant - plant 2

- 0/ -0/

2 90. -0/

9 ./0. .0/

0. ;0.

. .0. 0/

; 20/ ;0.

7 .0/ 0.

< 0/

;0.


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ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

"able 2

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initial set &mins( 2< da# strength &M8a(

'aborator#- 'aborator# 2 'aborator# - 'aborator# 2

-9/ -2 70


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!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

0 "he results in "able 9 have been obtained on tests on a set of concretes made

1ith the same aggregates and the same 8ortland cement0

a0 )hat conclusions can #ou ma!e about the use of strength tests at 9 da#s

for predicting 2< da# strength for 5ualit# control purposes=

b0 *ompare and contrast the relationships bet1eeni0 the mi% proportions and the measured properties

ii0 the ultrasonic pulse velocit# and compressive strength

1ith e%pected or t#pical relationships0

"able 9

mi% proportions &!gm9( properties

cementfree

1ater

aggregate 2/&SS>(

aggregate /&SS>(

slump&mm(

cube strength&M8a(

ultrasonic pulsevelocit# at 2<

da#s

&!msec(

9

da#s

2<

da#s.// -/ ---/ ./ 7. 9-0. .;0. 0


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"ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

++++++++++++++++++++++++++++++++++++++

• 4n #our ans1ers #ou should clearl# set out #our reasoning3 calculations and

assumptions etc0 throughout0

• Overall maximum length 7000 words &e%cluding report title page3 contents3

reference list and appendices3 but including 1ords in tables( 1ith each diagram3figure etc0 1ithin the main te%t to count as -./ 1ords0

• Ke# diagrams3 figures etc0 should not be relegated to appendices0

• umber of 1ords or 1ord e5uivalents should be declared on the title page0

D"6:

"his assignment consists of a progressive set of 5uestions3 and therefore 1e

suggest that all members of the group focus on each 5uestion in turn3 and agree on

the ans1ers before proceeding to the ne%t 5uestion0

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#ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

Table of ontents! "age

#$ Statistical anal%sis on results obtained from testing concrete

samples for modulus of elasticit%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6

#$# &ntroduction$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6

#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$6

#$( x $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$7

#$($# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$)

#$($#$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$)

#$($#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$*

#$($#$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#0

#$4 x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#'

#$4$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#'

#$4$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#+

#$4$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#7

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Table of ontents cont! "age

'xxxxx$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ #)

'$# &ntroduction$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)

'$' xx$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)

'$'$# xx$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)

'$'$#$# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#)

'$'$#$' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#*

'$'$#$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'0

'$'$' x $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'#

'$( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'6

'$($# x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'6

'$($' x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'7

'$($( x$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'7

'$4 onclusion$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'*

,eferences!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(0

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$ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

#$ Statistical anal%sis on results obtained from testing concrete

samples for modulus of elasticit%$

#$# &ntroduction

"he modulus of elasticit# re5uired for a high+rise building is / G8a0 "his 6 value is

re5uired for deflection control0 Statistical evaluation should be done to prove both

normal distribution of the data

'$ Anal%sis on reproducibilit% between two concrete plants$

'$# &ntroduction

90 Repeatabilit# and Reproducibilit# tests on setting times and 2< da# strengths of a

single batch of cement using t1o different laboratories0

Batch No.

28 Days ConcreteStrengths(Mpa)

Pant 1 Pant 2

1 !% !1

2 %&" !1

3 "0&" !"

4 !!&" !#&"

5 "!&" !!6 !2 !#&"

7 "! !!

8 !%

! !#&"

Me"#an !% !!&"

Co$nt 7 %

SD "&$" 2#

S%aest %&" !1

&argest "!&" !%

"' 1" $

Pant 1D#str#$t#on

C$r*e

Pant 2D#str#$t#on

C$r*e

Pant1 B#n

+re,$ency

Pant1 B#n

+re,$ency

%&" 1 !1 2!2 1 !1&" 0

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%ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

!!&" 1 !2 0

!7 0 !2&" 0

!%&" 0 ! 0

"2 0 !&" 0

"!&" 1 !! 2

!"&" 0

!# 0

!#&"

!7 0

!7&" 0

!$&" 0

!%& 1

-ae 2.

Variable 1 Variable 2

Mea' !$ !"

ara'*e ! 7

Ob+ervao'+ 7 %-./oe+e Mea'34ere'*e 0

f $ Sa 1&20%2#0

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P(T56) o'ea8 0&10"!2

Cr*a8 o'ea8 1&$"%"!$

P(T56) 9oa8 0&2#10$"

Cr*a8 9oa8 2&0#00!

' $-a.$' omparison population of means

HO 1 / 2 Te '88 ./oe++ e. are e +ame +re'

H1 1 0 2 Te a8er'ave ./oe++ e. are4ere'

Pant 1 Pant 2

SE 6 n SE 6 n

6 "&$";e'*e 'erva8 a "=8eve8

Pant 1 t *a$e / 7 1 Pant 2 t

*a$e / ! 1

/ 6 / 8

there'ore t*a$e 'or5 o' 'ree"o%

there'oret*a$e 'or

5 o' 'ree"o%(26) (28)

/ 5.14 / 4.46

t *a$e 9 S: / 5.14 9 2.21t *a$e 9 S:

/ 4.46 .887

there'ore;11.36 'or pant1 /

;3.!6'orpant 2

erefore fo88o9+ a e e+mae of e /o/8ao' mea' from e +am/8e mea'?

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@or P8a' 1 + !$ 11&#

a + ra'ge+ from #! o"%&#

@or P8a' 2 + !" &%#

a + ra'ge+ from !1&0! o!$&%#

The ranges for Plant 1 and Plant 2 do not overlap at the 95% condence level and therefore

conclude that population means are dierenteg! there is a signicant dierence in the concr

"o #e re$ect the ull H&pothesis!

20b( As per anal#sis done above 3the standard deviation and population mean for 8lant - is too hi *oncrete 5ualit# 1ill be compromised and this can increase production costs3 because target st

b# characteristic strength plus standard deviation times ! factor0

Batch records must be retrieved and evaluated for compliance0

Scales and plant e5uipment 1ill to be calibrated

Ra1 materials at the plant must be sampled and tested0

"rial mi%es must done to assess 1ater demand0

Batch 8lant personnel must be re+trained0

"ruc! mi%er inspections must the done

*ompliance to sampling 3cube ma!ing and crushing procedures 1ill have to be assessed

'aborator# staff 1ill have to be retrained

($0&ntroduction

( Assumptions

"he follo1ing are the assumptions for this 5uestionE

• "he cement sample ta!en from the batch follo1s a normal distribution curve

• "he cement sample provided to both laboratories has the same mean and

standard deviations

• "he e5uipment in both laboratories is of the same 5ualit# and same 4SD

certification

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($# Statistical anal%sis of the data

*onsidering that in both laboratories3 -/ observations 1ere made on initial setting

time and -2 observations 1ere made on 2< da# strength3 the data 1ill be anal#$ed

b# "+test and ,+test0 Belo1 is the data presentation0

Table #! Observation for /ab # /ab '

4nitial set &mins( 2< da# strength &Mpa(

Sample

F 'aborator# - 'aborator# 2 'aborator# -

'aborator#

2

- -9/ -2 70


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1igure #! omparison of &nitial set for /ab # /ab '

According to 6 -;+-3 the initial set for the cement had to greater than ;/ minutes

&Ref(3 both laboratories have sho1n that the cement is clearl# above its initial set

time0

*onsidering for "+test and ,+testE

2ull h%pothesis: "he means from the laboratories are e5ual &"+test(

Alternative h%pothesis: "he means from the laboratories are not the e5ual

2ull h%pothesis! "he variances from both laboratories are e5ual &,+test(

Alternative h%pothesis! "he variances from both laboratories are not e5ual

4n both cases H /0/. for .I confidence level

"esting the data as paired "+test3 the follo1ing results 1ere obtainedE

Table '! t3Test "aired Two Samples of eans

t+"est: 8aired "1o Sample for Means

Lab 1 Lab 2

Mean -9-0 -2902ariance 2/0/ -;0-777777<

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1!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

Dbservations -/ -/

8earson *orrelation /0/./..ifference /

df

t Stat 02--97/-

8&"Ht( one+tail /0///


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1"ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

1igure '! omparison of the two laboratories ') da% strengths

,ollo1ing the same null and alternative h#potheses mentioned above3 the paired t+

test gives the follo1ing results are obtainedE

Table (! t3Test paired two sample for ') da% strength means

t+"est: 8aired "1o Sample for Means

Lab 1 Lab 2

Mean .0-.


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1#ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

Since 8 &"Ht( is greater than /0/. &(3 1e re?ect the null h#pothesis and the means

are not e5ual hence significantl# different0

"esting the variance using the ,+test 1e find the follo1ingE

,or initial setE

Table 4! 13test Two 3 Sample &nitial Set 5ariance

,+"est "1o+Sample for ariances

Lab 1 Lab 2

Mean -9-0 -2902

ariance 2/0/ -;0-777777<

Dbservations -/ -/

df

, -029/-/


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,or the initial set3 1e re?ect the null h#pothesis3 the variances are significantl#

different and for the 2< da# strength3 1e accept the null h#pothesis3 the variances

are significantl# the same &e5ual(0

($' iscussion and onclusion

"he table belo1 sho1s a summar# of the situation

Table 6! Summar% of t3test and 13test anal%sis

"+test out come ,+test out come

*omparison of lab - and

lab 2 on initial set

Significantl# the same

means

Significantl# different

variances

*omparison of lab - and

lab 2 on 2< da# strength

Significantl# different

means

Significantl# the same

variance

Going bac! to figures - and 2 1e see that for the initial set &fig -(3 both laboratories

and uncontrollable variances 1hich agrees 1ith the ,+test findings0 "his might have

been because both laboratories had ine%perienced technicians carr#ing out the test0

,rom fig 23 2< da# strength3 1e see that laborator# 2 had a better controlled series of

results than laborator# -0 "he variance is 1ell controlled and consistenc# is

maintained in lab 20 "his is 1h#E the means of the t1o laboratories differ0 4t could be

interpreted that lab 2 had competent personnel to carr# out this test or had a better

5ualit# control monitoring s#stem as compared to lab -0

Based on the above evidence3 both laboratories have poor monitoring s#stems

orand less competent personnel to carr# out initial set tests and laborator# 2 has a

better monitoring s#stem orand competent personnel to carr# out 2< da# strength0

Luestion 9

b("he standard deviation for 8lant - is too high3compared to 8lant 20

"herefore the follo1ing 1ill have to be done0

• Batch records 1ill have to be evaluated for compliance0

• Scales and plant e5uipment 1ill have to be calibrated0

• Ra1 materials 1ill have to be sampled and tested0

• "rial mi%es 1ill be done to assess 1ater demand

•

8lant personnel 1ill have to be re+trained• "ruc! mi%er inspection 1ill have to be conducted0

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1$ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

• *ompliance to sampling 3cube ma!ing and crushing procedures 1ill have to

be assessed0

• 'aborator# staff 1ill have to be re+trained0

4. Concrete %a"e


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1%ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

@gre Jo9 9aer *eme' rao

*eme'

free9aer B;C

*be +re'g(MPa) +8m/ Sre'g

Ga'

a.+

2$a.+ (mm)

10 17" 0&"# 1&$ 7&" !0 7=

10 17" 0&"# 2&1 7&" "0 #2=

10 1%" 0 1!&% 0&$ $" !$=

2"" 170 0 1%&$ 0&1 0 ##=

22" 1#" 0&7 7&2 1$&2 0 !0=

2$" 210 0&7! 10&1 17&" 1$0 "$= S3 o'

+re'gga'

2"" 1%0 0&7" 1"&" 22&" #0 #%=

22" 170 0&7# %&2 1$&7 20 !%=Averag

e "= 11&$% Tab8e -g 9aer *eme' rao

@gre -g 9aer *eme' rao

Conc$s#ons

Page 1! of 24


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Tere + a eafe'e *orre8ao' be9ee' e ear8. age +re'g a' e

2$a. +re'g of *o'*ree& -o9ever e a. re+8 a+ a bg varab8.

e o fa*or+ 8De e +8m/& Te +'g a 7 a. re+8+ a+ a /re*o' +

more 9e8. +e ' '+r.&

Te +e of +a+*a8 /rogram+ a 9orD 4ere' e+g' +re'g ba*D oo'e e+g' +re'g 8De a 2"MPa + a8+o +e& T+ a88o9+ e Ka8.

/er+o' o more ea+8. +ee f ere + a /rob8em 9 e *o'*ree&

4..#. M#9 proport#ons an" %eas$re" propert#es

4..##.>trason#c p$se *eoc#ty (>P?) an" co%press#*e strength.

m /ro/oro'+ (Dg;m) /ro/ere+

*eme'

free9aer 9;*

*be +re'g(MPa) 8ra+o'* /8+e ve8o*. a 2$ a.+

a.+

2$a.+ (Dm;+e*)

"!" 20" 0&$ 22&$ !7&% !&7

"00 1%0 0&$ 1&" "#&" !&$

"!" 22" 0&!1 2&" !%&" !&72

%0 1%" 0&"0 1&2 "&2 !"

%0 200 0&"1 20&! !0&2 !"

%0 20" 0&" 2%&1 !! !&7"

10 17" 0&"# 1&$ 7&" !

10 17" 0&"# 2&1 7&" !&72

10 1%" 0 1!&% 0&$ !&""

2"" 170 0 1%&$ 0&1 !&!"

22" 1#" 0&7 7&2 1$&2 !&"

2$" 210 0&7! 10&1 17&" !&2

2"" 1%0 0&7" 1"&" 22&" !&"2

22" 170 0&7# %&2 1$&7 !&$ Tab8e UP a 2$3a. +re'g

Page 2 of 24


21/24


@gre 2$3a. UP aga'+ B;C rao

@gre 2$3a. Cbe +re'g aga'+ B;C rao

Tere + obvo+8. a 'ee for a re8ab8e 'o'e+r*ve e+ meo o

*om/8eme' or re/8a*e e e+'g e+r*ve mea'+ of verf.'g e

+re'g of *o'*ree ' Ke+o' o' +e& Te UP + o9ever 'o *rre'8.

+e a+ e /rmar. meo of e+'g, b +e a+ a +//8eme'ar.

'*aor of e Ka8. of *o'*ree ' +r*re+& T+ + be*a+e e

re8ao'+/ be9ee' *om/re++ve +re'g of *o'*ree a' UP + 'o

+m/8e& (LL Poo', 1%%)

Page 21 of 24


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Te aggregae ./e a' e amo of aggregae a + ++/e'e ' e

*o'*ree a+ a bg e4e* o' e re+8+ a are a*eave 9 e UP

meo+& (& J', 200)

Be' av'g a 8ooD a e 2$a. UP a' e 2$a. +re'g *om/are o

e 9;* o'e *a' +ee a +'* re8ao'+/&

Conc$s#on

Tere + a '*ao' a e UP *a' be +e for e /re*o' of e

2$a. +re'g o' +e& Tere + o9ever a fe9 +or fa88'g+:

a& Te UP 988 ave o be *a8brae o' a +e*o' of D'o9' *o'*ree of e +ame maera8 a' *om/o+o'&

b& Te re8ao'+/ be9ee' *r'g a' e em/erare a 9* a//e'+ a8+o /8a.+ a /ar ' e varab8.& (& S', 200")

*& Te 8o*ao' a' +rbo' of .or re'for*e +ee8 ' e +r*re&

& Com/a*o' of e *o'*ree member

F. aD'g 'o *o'+erao' a88 e 4ere' /arameer+ I 9o8 +e e

UP +.+em+ o'8. a+ a' '*ao' a' a ver>*ao' +.+em or o e'f.

a /o++b8e /rob8ema* area ' .or +r*re&

a. B##ographyLL Poo', T& B& (1%%)& 3eve8o/eme' of +a+*a8 Ka8. a++ra'*e *rero' for

*o'*ree +'g UP meo+& '() *aterials +ournal , "#$"7&

Sear, J& (200)& a8. *o'ro8& I' F& S& & Ne9ma', 'dvanced (oncrete

Technolog& (//& %;1%;2!)& Ofor: Fer9or-ema''&

& J', C& J& (200)& Pre*o' of UP ' *o'*ree& '() *aterials +urnal , 212$&

& S', T& & (200")& Tem/erare e4e*+ o' +re'g eva8ao' of *eme' ba*e

9 8ra+o'* 9ave reQe*o' e*'ge& '() *aterials +ournal , 27227$&

Page 22 of 24


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+ onclusion$

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2!ASSIGNMENT 7: STATISTICS (November 2012), GROUP 22

,eferences!

2 2

group 22 assignment 7 draft

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