POPULATION PERCENTAGE PROBABILITY METHOD REPORT

8/14/2019 POPULATION PERCENTAGE PROBABILITY METHOD REPORT

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REG: 4142

NAME: MUHAMMAD YASIR SALEEM

COURSE: STATISTICS AND INFERENCE

PROGRAM: MBA

FACULTY: SIR SHAHBAZ KHAN

PROJECT REPORT:

TOPIC: POPULATION PERCENTAGE PROBABILITYMETHOD

DUE DATE: 15-APR-2009


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ACKNOWLEDGEMENT

I would like to thank our respected Statistics and inferenceteacher Mr. Shahbaz khan, for providing us the opportunity

of conducting a research on Students who are interested inwatching cable.

This project has provided us with great insight, knowledgeand experience about working on statistical data which willhelp us in our practical life to use different kinds of data in

order to bring statistical outcomes which are easy tounderstand by graph, charts, etc.

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CONTENTS

Pg. #

EXECUTIVE SUMMARY.01

INTRODUCTION..02

METHODOLOGY..03

FINDINGS..04

DISCUSSION AND INTERPRETATION

05

CONCLUSION AND RECOMMENDATION..06

REFERENCES07

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EXECUTIVE SUMMARY

We carried out a study on a selected random sample of 40students of which 20 were boys and 20 girls to calculate thelevel of satisfaction of students using the transportationservice provided by PAF-KIET INSTITUTE. It was found that45% of the boys and 60% of the girls are satisfied whereas,the rest are dissatisfied with the service. It is concluded thatwe can be 90% confident that the true percentage of PAF-

KIET boys who are satisfied is between 25.77 and 64.22percent. On the other hand, we can be 95% confident thatthe true percentage of PAF KIET girls who are satisfied isbetween 37.18 and 82.8 percent. Therefore, it isrecommended to arrange more points so that all dissatisfiedstudents can be accommodated comfortably and acquire thedue service they are paying for.

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INTRODUCTION

A large number of dissatisfied students complaint regardingthe transportation service provided by PAF-KIET INSTITUTEprompted the study. Both boys and girls complained thatthey do not get due service they are paying for i.e. a properseat to sit on, frequent absence of points and

mismanagement of time which makes them late for theirrespective classes. Resolution of this issue is importantbecause students are an asset for the institute and providingthem with ease and comfort is obligatory on themanagement. There is a critical need to formulate a courseof action as dissatisfaction of students in regard totransportation service will give way to alternative ways i.e.private conveyance or public transport. Undoubtedly thelatter action will cause a great loss for the management of

the institute. Therefore, a study was conducted to find outhow many students are satisfied so that work can be doneon the remaining who are dissatisfied and overcome theproblem successfully.

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METHODOLOGY

Since the mean of the sampling distribution of percentagesis equal to the population percentage, the sample

percentage (p) is an unbiased estimator of the populationpercentage ( ). If the sample size is sufficiently large thatis, if np [ the sample size (n) times the sample percentage(p) is 500, and if n(100-p) is also 500 then thesampling distribution of p approximates the normaldistribution. Thus, we are able to make probabilitystatements about the interval estimate of ^ that are basedon sample percentages.

We use p, the sample percentage, as the point estimate for^ and construct the interval estimate of the populationpercentage as follows:

p z /2 p < < p + z /2 p

LOWER CONFIDENCE UPPER CONFIDENCE

LIMIT LIMIT

A z value is used here in exactly the same way it was used toestimate populations mean. And when we compute a valuefor p, we have produced an estimate of the standard

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deviation of the sampling distribution of percentages thatis, an estimate of the standard error of percentage. It may befound this way:

p = p(100 p)n

With the help of POPULATION PERCENTAGEPROBABILITY METHOD we will complete the study for thedata given as follows:

BOYS

Sr. # NAMES SATISFIEDDISSATISFIED

01. ASAD 02. ALI 03. ASHAR 04. AHMED

05. BAKIR 06. BABAR 07. AKBAR 08. NOMAN 09. ADEEL 10. DANIYAL 11. TAHA

12. AQIL

13. AHSAN 14. FARHAN 15. NASIR 16. SAMEER 17. MAZHAR 18. TAUQEER

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19. FAIZAN 20. PRAKASH

%No. of boys satisfied: 09 45

No. of boys dissatisfied: 11 55

GIRLS

Sr. # NAMES SATISFIEDDISSATISFIED

01. AMNA 02. MEHWISH 03. ZARISH 04. RAFIA05. HIRA

06. QURATULAIN 07. SOBIA 08. SEHAR09. YUMNA 10. DANIYA11. FAREHA 12. HIBA 13. SUNIYA 14. SAMRAH15. SANA16. HINA

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17. SARA18. AISHA 19. FATIMA

20. ARSALAN

%

No. of girls satisfied: 12 60

No. of girls dissatisfied: 08 40

FINDINGS

PERCENTAGE PROBABILITY

SATISFIED BOYS:

p = 45 v = n 1 C.I. = 90%n = 20 = 20 -1 = 0.9 -1

= 19 = 0.1/2t = 0.05

p = p(100 p)n

p = 45(100 45)20

p = 2475

20

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p = 10.9%

With a confidence level of 95 percent, the t value = 2.093.There fore, the interval estimate is

= p t p < < p+ t p

= 60 (2.093) (10.9) < < 60 + (2.093) (10.9)

= 37.18 < < 82.8 percent

So we can be 95 percent confident that the true percentageof PAF KIET girls who are satisfied is between 37.18 and 82.8percent.

DISCUSSION AND INTERPRETATION

From the facts and figures we have calculated in theprevious section, it is evident that we can be 90% confidentthat boys are satisfied between the range of 25.77 and 64.22percent and the rest are dissatisfied. Whereas we can be95% confident that girls are satisfied between the range of37.18 and 82.8 percent and the remaining are dissatisfied.

Hence, we have worked out the population percentage ofstudents who are satisfied with the transportation serviceprovided by PAF KIET INSTITUTE which will help us come upwith a recommendation for the management to improvetheir services for those students who are dissatisfied.

CONCLUSION AND RECOMMENDATION

Therefore, we conclude that the transport managementshould arrange more points to satisfy 55% of the boys and40% of the girls who are dissatisfied. The latter action must

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be taken in order to avoid loss and provide due service to thestudents for which they are paying a handsome amount.

REFERENCES

Online help:

http://www.betterwritingskills.com/articles/reports-article.txt

Book:

A FIRST COURSE (6th Edition) by Sanders & Smidt

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