Stats Project PP

8/8/2019 Stats Project PP

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1) M. IMRAN NAZIR1) M. IMRAN NAZIR

(52800)(52800)

2) FARHAN SAYEED2) FARHAN SAYEED

(52821)(52821)

3) ZAIN AHMED3) ZAIN AHMED

(52814)(52814)

4) OWAIS SHAH4) OWAIS SHAH(53173)(53173)

STATISTICS & INFERENCESTATISTICS & INFERENCEProject On: Poultry IndustryProject On: Poultry Industry

Submitted To: Sir SHAHBAZ KHANSubmitted To: Sir SHAHBAZ KHAN

Course ID: 53576Course ID: 53576


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BACKGROUNDBACKGROUND

Its about the Poultry Industry of Pakistan.Its about the Poultry Industry of Pakistan. Involves two major and dominance companiesInvolves two major and dominance companies

i.e. Hii.e. Hi Tech Group of Companies (Pvt) LtdTech Group of Companies (Pvt) Ltd

and K&NS.and K&NS. Information is collected by deliberately visitingInformation is collected by deliberately visiting

of their respective offices.of their respective offices.

The main objective is to find out the averageThe main objective is to find out the averagegrowth and revenue as well as theirgrowth and revenue as well as theirestimation and hypothesis of the firms andestimation and hypothesis of the firms and

Poultry Industry.Poultry Industry.


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BACKGROUNDBACKGROUND

WHY CHOOSING POULTRY INDUSTRY:WHY CHOOSING POULTRY INDUSTRY: --

Tax free Industry.Tax free Industry.

Prompt return of Investment.Prompt return of Investment. Rising consumers demands.Rising consumers demands.

Income spending of population on food isIncome spending of population on food is

increasing.increasing. Fastest growing Industry now a days inFastest growing Industry now a days in

Pakistan.Pakistan.


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Growth in terms of ProductionGrowth in terms of ProductionThe main indicator is Broiler Chicks.The main indicator is Broiler Chicks.

Note: InXNote: InX Axeswe have progressive YearsAxeswe have progressive Years

AndinYAndinY Axeswe have quantityofBroilerChicks(inMillions)Axeswe have quantityofBroilerChicks(inMillions)

0

1000

2000

3000

4000

5000

6000

2001 2003 2005 2007 2009

Production

Growth


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DATA Analysis of HiDATA Analysis of Hi Tech Group (in termsTech Group (in terms

of % of revenue)of % of revenue)


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DATA Analysis of HiDATA Analysis of Hi Tech Group (inTech Group (interms of % of revenue)terms of % of revenue)

Chicks

Feeds

Medicine

Farm

Constructi

on


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DATA Analysis of K&NS (in terms of % ofDATA Analysis of K&NS (in terms of % of

revenue)revenue)

Chicks

Chicken

Product


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Information Gathered from both theInformation Gathered from both the

CompaniesCompanies

The core product is Broiler Chicks. The data is analyzed on that bases.The core product is Broiler Chicks. The data is analyzed on that bases.


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ZZ ScoreScore [Standard Score][Standard Score] YearYear

By Year:By Year: --

2001: Z =2001: Z = -- 0.390.39 2002: Z =2002: Z = -- 0.370.37

2003: Z =2003: Z = -- 0.380.38

2004: Z =2004: Z = -- 0.720.72 2005: Z =2005: Z = -- 0.190.19

2006: Z =2006: Z = -- 0.120.12

2007: Z =2007: Z = -- 0.180.18

2008: Z =2008: Z = -- 0.270.27

2009: Z = + 2.622009: Z = + 2.62


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epresentat on oepresentat on o core n ormacore n ormaCurve from 1st Year (2001) to Ninth YearCurve from 1st Year (2001) to Ninth Year

(2009)(2009)


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Estimation of Chicks RatesEstimation of Chicks Rates


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Confidence interval of True MeanConfidence interval of True Mean

As we have gathered data of last nine year'sAs we have gathered data of last nine year'sfluctuation. So the 99% confidence interval offluctuation. So the 99% confidence interval ofthe true mean would be:the true mean would be: --

DATA:DATA:--

Confidence level, CL = 99%.Confidence level, CL = 99%.

Number of Years, n = 9.Number of Years, n = 9.

Mean, x` = 18.89Mean, x` = 18.89Standard deviation, s = 14.04Standard deviation, s = 14.04

The value of z (nThe value of z (n--1) = 3.3551) = 3.355


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Confidence interval of True MeanConfidence interval of True Mean

The formula we have is:The formula we have is:--x`x` tv=ntv=n--1 (s / n) < u < x` + tv=n1 (s / n) < u < x` + tv=n--1 (s / n)1 (s / n)

Putting values and then solving it:Putting values and then solving it:18.8918.89 3.355 (14.04 / 9) < u < 18.89 + 3.355 (14.04 / 9)3.355 (14.04 / 9) < u < 18.89 + 3.355 (14.04 / 9)

3.1886 < u < 34.59143.1886 < u < 34.5914

Hence, we can say that, with 99% confidence,Hence, we can say that, with 99% confidence,the true mean of chick's rate is between 3.1886the true mean of chick's rate is between 3.1886

and 34.5914.and 34.5914.


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Confidence interval of PopulationConfidence interval of Population

ProportionProportion

If we want to consider last three year's analysisIf we want to consider last three year's analysisout of given nine years, the 99% confidenceout of given nine years, the 99% confidenceinterval of population proportion is:interval of population proportion is:--

DATA:DATA:--p^ = x / n = 3 / 9, = 0.33p^ = x / n = 3 / 9, = 0.33

q^ = 1q^ = 1 p^ = 1p^ = 1 0.33, = 0.670.33, = 0.67

n = 9 (years).n = 9 (years).

Confidence Level = 99%.Confidence Level = 99%.

The value of z (nThe value of z (n--1) = 3.355.1) = 3.355.


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Confidence interval of PopulationConfidence interval of PopulationProportionProportion

The formula available is:The formula available is:--

Putting the values and solving it:Putting the values and solving it:

0.195 < p < 0.85510.195 < p < 0.8551

Hence, we can say that, with 99% confidence that theHence, we can say that, with 99% confidence that thetrue population percentage of chicks rate of the lasttrue population percentage of chicks rate of the lastthree years is between 19.50% and 85.51%.three years is between 19.50% and 85.51%.


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HYPOTHESIS TESTING FOR HYPOTHESIS TESTING FOR

Consider the scenario that the average rate of chick isConsider the scenario that the average rate of chick ismore than Rs 25/chicks. We took the random samplemore than Rs 25/chicks. We took the random sampleof last 30 months average rate of chicks which is Rsof last 30 months average rate of chicks which is Rs29.06/chick. The value of = 0.10 and the standard29.06/chick. The value of = 0.10 and the standard

deviation is 14.04 (calculated above).deviation is 14.04 (calculated above).The given data is:The given data is:--

= 25 = 25

x`= 29.06x`= 29.06

n = 30 (months)n = 30 (months)

= 0.10 = 0.10

s = 14.04s = 14.04


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Step # 01:Step # 01: --

Ho:Ho: 25 And 25 And H1:H1: > 25 (Claim) > 25 (Claim)

Step # 02:Step # 02: --

The value of = 0.10; the test is right tailedThe value of = 0.10; the test is right tailedtest. The critical value is z = +1.282.test. The critical value is z = +1.282.

Step # 03:Step # 03: --

= + 1.58= + 1.58


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Step # 04:Step # 04: --

As z cal lies in the rejection region, so reject the HoAs z cal lies in the rejection region, so reject the Ho

Step # 05:Step # 05: --There is not enough evidence to support theThere is not enough evidence to support theclaim that average rate of chicks is more thanclaim that average rate of chicks is more thanRs 25/chicks.Rs 25/chicks.


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HYPOTHESIS TESTING FOR POPULATIONHYPOTHESIS TESTING FOR POPULATION

PROPORTIONPROPORTION

To perform the hypothesis testing for population proportion,To perform the hypothesis testing for population proportion,suppose the poultry firms are not fulfilling even 25% of theirsuppose the poultry firms are not fulfilling even 25% of theircustomer's demand. We took the random sample of 30 partiescustomer's demand. We took the random sample of 30 parties

out of their 50 parties. The value of = 0.010:out of their 50 parties. The value of = 0.010:--

The given data is:The given data is:--

p = 25% i.e. 0.25p = 25% i.e. 0.25

= 0.010 = 0.010p^ = x/n i.e. 30/50, = 0.6p^ = x/n i.e. 30/50, = 0.6

q = 1q = 1 p i.e. 1p i.e. 1 0.25, = 0.750.25, = 0.75


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HYPOTHESIS TESTING FOR POPULATIONHYPOTHESIS TESTING FOR POPULATIONPROPORTIONPROPORTION

Step # 01:Step # 01: --Ho:Ho: p 0.25 (Claim) Andp 0.25 (Claim) And H1:H1: p = 0.25p = 0.25

Step # 02:Step # 02: --

The value of = 0.010; the test is two tailedThe value of = 0.010; the test is two tailedtest. The value is between +2.576 andtest. The value is between +2.576 and --2.5762.576

Step # 03:Step # 03: --

Z = 18.07Z = 18.07


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HYPOTHESIS TESTING FOR POPULATIONHYPOTHESIS TESTING FOR POPULATIONPROPORTIONPROPORTION

Step # 04:Step # 04: --

As z calculation lies in the rejection region, so reject Ho.As z calculation lies in the rejection region, so reject Ho.

Step # 05Step # 05There is no enough evidence to support the claim thatThere is no enough evidence to support the claim thatpoultry firms are not fulfilling even 25% of the totalpoultry firms are not fulfilling even 25% of the totaldemand of the customersdemand of the customers


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GOODNESS OF FIT TESTGOODNESS OF FIT TEST

To perform the goodness of test, suppose thereTo perform the goodness of test, suppose thereis a scenario that new customers are notis a scenario that new customers are notshowing the preference towards the Poultryshowing the preference towards the PoultryIndustry because of shortage of supply:Industry because of shortage of supply:


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Step # 01:Step # 01: --Ho: New customers are Not showing the preference towards theHo: New customers are Not showing the preference towards thePoultry Industry. (Claim)Poultry Industry. (Claim)

H1: New customers are showing the preference towards theH1: New customers are showing the preference towards the

Poultry Industry.Poultry Industry.Step # 02:Step # 02: --

The value of = 0.005. The degree of freedom is 9The value of = 0.005. The degree of freedom is 9--1 = 8.1 = 8.The critical value is 21.955.The critical value is 21.955.

Step # 03:Step # 03: --22Y cal = [ (OY cal = [ (O E) / E]E) / E]

22

Y cal = 83.54Y cal = 83.54


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Step # 04:Step # 04: --

As chi square value lies in the rejection region, so reject Ho.As chi square value lies in the rejection region, so reject Ho.

Step # 05:Step # 05: --

There is no enough evidence to support theThere is no enough evidence to support theclaim that the new customers are notclaim that the new customers are notshowing any preference towards the Poultryshowing any preference towards the Poultry

industry.industry.

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