Chap 3

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Data Description

The relation between different variables can be easily perceived by condensing the data. The

distribution of Drivers, Constructors and Tyre suppliers is shown as:

Tyre Supplier

Constructors

Bridgestone

Michelin

Pirelli

DriverCount

Ferrari 8 3 3 14

Honda 6 4 3 13

Mclaren 3 5 3 11

Mercedes 7 7 2 16

Red Bull 5 9 6 20

Renault 7 2 4 13

Williams 3 3 7 13

DriverCount 39 33 28 100

0123

456789

108

6

3

7

5

7

334

5

7

9

2

33 3 3

2

6

4

7

Construtor and Tyre Distriution a!ong Drivers

Bridgestone

Micelin!irelli

"onstructors

#ri$er "ount

As the down force, break wear, tyre wear and fuel load varies across cars, it is a good idea toknow how they are distributed. The tables and charts depicted below shows the how they vary.

Brea" #ear $evelDo%n&orce$evel

'igh $o% Mediu!

CarCount

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Hig 4 6 11 21

%o& 6 10 7 23

Medium 6 10 5 21

'er( Hig 5 9 4 18

'er( %o& 7 5 5 17

Car Count 28 (0 32 100

Hig %o& Medium 'er( Hig 'er( %o&0

2

4

6

8

10

12

4

6 6 5

7

6

10 109

5

11

7

54

5

'ariation o) #o&n)orce le$el &it Brea* Wear

Hig

%o&

Medium

#o&n)orce %e$el

"ar "ount

Tyre #ear $evel)uel$oad

'igh

$o%

Mediu!

CarCount

Hig 6 6 5 17

%o& 7 11 6 24

Medium 9 9 11 29'er(Hig 4 7 3 14'er(%o& 6 7 3 16

CarCount 32 (0 28 100

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Hig %o& Medium 'er( Hig 'er( %o&0

2

4

6

8

10

12

67

9

4

66

11

9

7 7

56

11

3 3

'ariation o) +(re Wear &it Fuel %oad

Hig

%o&

Medium

Fuel %oad

+(re Wear

With the variation of wins across constructors suggested from the previous seasons, we can

determine the probability that a constructor would win the world championship. A good estimate

of wins in a season of !" races would suggest in a greater likelihood of achieving that target.#robabilities for the same are as follows:

Constructors

#ins

#inningProaility

Proaility o& atleast ( #ins

Ferrari 338 0,1385 0,2970

Honda 335 0,1373 0,2913

Mclaren 292 0,1197 0,2114

Mercedes 380 0,1557 0,3800Red Bull 465 0,1906 0,5466

Renault 297 0,1217 0,2201

Williams 333 0,1365 0,2875*randTotal

2((0

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The chance for each constructors to win races in the championship can be e$pressed as %inomial

distribution. The %inomial curve for the ! contenders&'errari and (ercedes are shown:

0 5 10 15 20 250,0000

0,0500

0,1000

0,1500

0,2000

Binomial "ur$e - Wins )or Red Bull

Race Wins

"ance )or Wins

0 5 10 15 20 250,0000

0,0500

0,1000

0,1500

0,2000

Binomial "ur$e - Wins )or Mercedes

Race Wins

"ance )or Wins

)ince the likelihood for or more wins varies only a slightly among the other * constructors, the binomial curve only varies slightly from that of that of (ercedes, showing a declining trend.

The D+'s measure the number of instances where a car failed to finish the race. The factors that

leads to such accidents are a function of driver error. 'rom the sample of -"" drivers, the

calculated average number of accidents is:

Mean.tarts

279,66

Mean 36,2

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#/Fs 5

n a season of !" races it can be said that there will be an average of !./ accidents in a season. n

order to improve the reliability, new regulations will be introduced by 'A if there are more than0 accidents within the ne$t * seasons.

This follows a #oisson distribution as shown:

Poisson Probabilities

DataMean nu!er o&accidents per season 2+,

- .alue 8

/esults

P840+0038

0 5 10 15 20 250,0000

0,0500

0,1000

0,1500

0,2000

0,2500

0,3000

ccidents o$er 5 (ears

/umer o) accidents

"ance )or ccident

The chance for 0 accidents over * seasons 1 ".""20

The mean pit stop time for cars from the data is seconds. This follows an e$ponentialdistribution. The chance that a car takes more than 3 seconds is then 0!./!4.

Exponential Probabilities

DataMean ti!e &or pitstops (+0 s

- .alue 5+0 s

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/esults

P6540+82

,2

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5

0,0000

0,1000

0,2000

0,3000

0,4000

0,5000

0,6000

0,7000

0,8000

0,9000

!it sto time #istriution

!it sto time in seconds

"ance )or te it sto time

Inferential Data Analysis

Constructors, 5ace engineers, and media surrounding the sport make several claims and

predictions based on the previous results. n this section inferential statistics is used to predict

with reasonable certainty whether the same is true. The sample of -"" drivers and thecorresponding parameters taken in this study is a good representation of the generali6ed history

of 'ormula -. To address the assumptions of these claims, various tests of significance are done.

All tests are conducted with *4 7evel of )ignificance.

Test 1

ccording to te F1-standards i) te a$erage seed o) all te racers

trougout all te las )alls elo& 198 m ten tere can e a denite

ualit( degradation issue &it te engine and te current engine needs to e

migrated to a ne&er $ersion, samle o) a 100 F1 racers as een collected

to see i) tere is a need to relace te current '6 $ersion engine &it a

ne&er '8 $ersion,

Solution:

The hypothesis can be formed as,

8" : 9 1 -0 mph v;s 8- : 9 < -0 mph

)ince sample si6e, n 1 -""", so we have a large sample.

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7 Test o& 'ypothesis &orthe Mean

Dataull 'ypothesis

198$evel o& Signicance 0+0:Speed StandardDeviation

10+1,

Sa!ple Si;e 1000

Sa!ple Mean19,+

3

ntermediate"alculations.tandard rror o) teMean

0,32128741

7 Test Statistic

-5,2912126

2

%o&er-+ail +est

%o&er "ritical 'alue

-1,6448536

27

p<.alue 6,0754-08

/e=ect the nullhypothesis

)ince the p&value is less than =, so we re>ect the null hypothesis.)o, we can conclude that there is definite ?uality degradation issue with the engine and hence the

current version of @/ engine should be migrated to the higher @0 version.

Test 2

#uring 2001-2010 seasons te cars tat used !irelli t(res recorded a it sto

time o) 5 seconds, "onstructors assume tat &it te recent cange in t(reregulations tere is a decrease in it sto time,

The hypothesis can be formed as,

8" : 9 1 * seconds v;s 8- : 9 < * )econds

)ince sample si6e, n 1 !0, so we have a small sample

t Test &or 'ypothesis o&

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the Mean

#ata/ull H(otesism 5

%e$el o) .ignicance 0,05.amle .i:e 28

.amle Mean4,007142

857

.amle .tandard #e$iation0,435404

088

ntermediate "alculations

.tandard rror o) te Mean0,082283

638

#egrees o) Freedom 27

t +est .tatistic

-12,06627

665

%o&er-+ail +est


-1,703288

446

-'alue1,09381

-12

/e=ect the nullhypothesis

)ince the p&value is less than =, so we re>ect the null hypothesis.Hence &e can conclude tat &it te recent cange in regulations tere is a

signicant decrease in it sto time,

Test 6

The new design of the tyres for the current season are supposed to increase the heat within -"

laps. The earlier the tyres are warmed up and reach the optimum temperature, better the gripthrough the corners and hence causes performance improvement. This grip is a function of the

cornering coefficient. Does the new tyres work as intended

The hypothesis can be framed as,

8" : 9' 1 97 v;s 8- : 9' < 97

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Paired t Test

#ataH(otesi:ed Mean

#i;erence 0%e$el o) signicance 0,05


.amle .i:e 28

#Bar -0,173809524

#egrees o) Freedom 27

.# 1,13574026

.tandard rror 0,214634734

t Test Statistic -0,809792154

<er-+ail +est

<er "ritical 'alue 1,703288446

p<.alue 0,787430336Do not re=ect the nullhypothesis t<Test> Paired T%o Sa!ple&or Means

Cornering 1<:$aps

Cornering ,<10$aps

Mean 5,322619048 5,496428571'ariance 4,60675338 2,804225456

=ser$ations 28 28

!earson "orrelation 0,851517565

H(otesi:ed Mean #i;erence 0

d) 27

t .tat -0,809792154

PT6t4 one<tail 0,212569664

t "ritical one-tail 1,703288446

!>+?t@ t&o-tail 0,425139329

t "ritical t&o-tail 2,051830516

TD?STCalculations

+,#.+,R+0,212

57

1-+,#.+,R+0,787

43

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)ince the p&value is greater than =, we do not re>ect the null hypothesis. t can thus be concluded

that the tyres do not work as intended.

Test 5

Bridgestone and Micelin are te 2 largest t(re suliers )or F1 and as eentrougout its istor(, s suc te sorts media ased on te rand imageclaim tat tere is no signicant di;erent et&een te roortion o) teset(res, s teir claim Austied

+e (otesis can e )ramed as

8" : #% 1 #( v;s 8- : #% B #(

TyresCount o&Driver

Bridgestone 39

Micelin 33

!irelli 28

*rand Total 100

7 Test &or Di@erences in T%oProportions

#ata

H(otesi:ed #i;erence 0

$evel o& Signicance 0,05

Bridgestone

/umer o) tems o) nterest 39

.amle .i:e 100

Micelin

/umer o) tems o) nterest 33.amle .i:e 100


Bridgestone !roortion 0,39

Micelin !roortion 0,33

#i;erence in +&o !roortions 0,06

$erage !roortion 0,36

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C +est .tatistic0,883883

476

+&o-+ail +est


-

1,959963985

<er "ritical 'alue1,959963

985

p<.alue0,376759

118Do not re=ect the nullhypothesis

)ince the p&value is greater than =, we do not re>ect the null hypothesis. t can thus be concluded

that there is no significant difference between the proportions of the ! tyres.

Test 10

random anal(sis o) te numer o) )astest las acie$ed ( cars runningte 3 t(es o) t(res D Bridgestone Micelin E !irelli suggest tat 40 o) te)astest las are ( Bridgestone 30 eac ( te oter 2, #oes te actualnumer o) )astest las di;er )rom tat o) te anal(sis done

+e (otesis can e )ramed as

H0 G +e roortion o) te )astest las are eual to G !B 0,4 !M 0,3 !

0,3s

H1 G +e roortions o) )astest las are not eual toG !B 0,4 !M 0,3 ! 0,3

Χ2 test o& *oodness o& )it

TyresSu! o& )astest$aps

Apected )ast$aps

ChiSuare

Bridgestone 895 927,6

1,145709357

Micelin 774 695,78,812548

512

!irelli 650 695,73,001997

988*randTotal 2319 2319

12+9,02::8,

P .alue 0+001:33,1(

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.ince te -$alue is less tan I &e reAect te null (otesis, +at is teactual numer o) )astest las di;er )rom &at is claimed,

Test 11

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