Population Percentage Probability Method Report

REG:

4142

NAME:

MUHAMMAD YASIR SALEEM

COURSE:

STATISTICS AND INFERENCE

PROGRAM:

MBA

FACULTY:

SIR SHAHBAZ KHAN

PROJECT REPORT: TOPIC: METHOD DUE DATE:

POPULATION PERCENTAGE PROBABILITY 15-APR-2009

ACKNOWLEDGEMENT I would like to thank our respected Statistics and inference teacher Mr. Shahbaz khan, for providing us the opportunity of conducting a research on Students who are interested in watching cable. This project has provided us with great insight, knowledge and experience about working on statistical data which will help us in our practical life to use different kinds of data in order to bring statistical outcomes which are easy to understand 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

•

REFERENCES………………………………………… 07

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EXECUTIVE SUMMARY We carried out a study on a selected random sample of 40 students of which 20 were boys and 20 girls to calculate the level of satisfaction of students using the transportation service provided by PAF-KIET INSTITUTE. It was found that 45% of the boys and 60% of the girls are satisfied whereas, the rest are dissatisfied with the service. It is concluded that we can be 90% confident that the true percentage of PAFKIET boys who are satisfied is between 25.77 and 64.22 percent. On the other hand, we can be 95% confident that the true percentage of PAF KIET girls who are satisfied is between 37.18 and 82.8 percent. Therefore, it is recommended to arrange more points so that all dissatisfied students can be accommodated comfortably and acquire the due service they are paying for.

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INTRODUCTION A large number of dissatisfied students complaint regarding the transportation service provided by PAF-KIET INSTITUTE prompted the study. Both boys and girls complained that they do not get due service they are paying for i.e. a proper seat to sit on, frequent absence of points and mismanagement of time which makes them late for their respective classes. Resolution of this issue is important because students are an asset for the institute and providing them with ease and comfort is obligatory on the management. There is a critical need to formulate a course of action as dissatisfaction of students in regard to transportation service will give way to alternative ways i.e. private conveyance or public transport. Undoubtedly the latter action will cause a great loss for the management of the institute. Therefore, a study was conducted to find out how many students are satisfied so that work can be done on the remaining who are dissatisfied and overcome the problem successfully.

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METHODOLOGY Since the mean of the sampling distribution of percentages is equal to the population percentage, the sample percentage (p) is an unbiased estimator of the population percentage ( ). If the sample size is sufficiently large – that is, if n×p [ the sample size (n) times the sample percentage (p) is ≥ 500, and if n(100-p) is also ≥ 500 – then the sampling distribution of p approximates the normal distribution. Thus, we are able to make probability statements about the interval estimate of ^ that are based on sample percentages. We use p, the sample percentage, as the point estimate for ^ and construct the interval estimate of the population percentage as follows: p–z

/2 δp <


LOWER CONFIDENCE LIMIT

/2 δp UPPER CONFIDENCE LIMIT

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

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deviation of the sampling distribution of percentages – that is, an estimate of the standard error of percentage. It may be found this way: δp = p(100 – p) n

With the help of POPULATION PERCENTAGE PROBABILITY METHOD we will complete the study for the data given as follows: BOYS Sr. # NAMES DISSATISFIED 01. 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. √ 12. √ 13. 14. 15. 16. 17. 18.

ASAD ALI ASHAR AHMED BAKIR BABAR AKBAR NOMAN ADEEL DANIYAL TAHA

SATISFIED √ √ √ √ √ √ √ √ √ √

AQIL AHSAN FARHAN NASIR SAMEER MAZHAR TAUQEER

√ √ √ √ √ √

7

19. 20.

FAIZAN PRAKASH

√ √

√

%

No. of boys satisfied:

09

45

No. of boys dissatisfied:

11

55

GIRLS Sr. # NAMES DISSATISFIED 01. 02. 03. 04. √ 05. 06. 07. 08. √ 09. 10. √ 11. 12. 13. 14. √ 15. √ 16.

AMNA MEHWISH ZARISH RAFIA

SATISFIED √ √ √

HIRA QURATULAIN SOBIA SEHAR

√

YUMNA DANIYA

√

FAREHA HIBA SUNIYA SAMRAH

√ √ √

√ √

SANA HINA

√

8

17. √ 18. 19. 20.

SARA AISHA FATIMA ARSALAN

√ √ √ √

%

No. of girls satisfied:

12

60

No. of girls dissatisfied:

08

40

FINDINGS PERCENTAGE PROBABILITY SATISFIED BOYS: p = 45 n = 20

v=n–1 = 20 -1 = 19

δp =

p(100 – p) n

δp =

45(100 – 45) 20

C.I. = 90% = 0.9 -1 = 0.1/2 t = 0.05

δp = 2475 20

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δp = √123.75 δp = 11.12%

With a confidence level of 90 percent, the t value = 1.729. There fore, the interval estimate is = p – t δp <

< p + t δp

= 45 – (1.729) (11.12) < = 25.77 <

< 45 + (1.729) (11.12)

< 64.22 percent

So we can be 90 percent confident that the true percentage of PAF KIET boys who are satisfied is between 25.77 and 64.22 percent. SATISFIED GIRLS: p = 60 n = 20

δp =

v= n -1 v= 20 – 1 v= 19

C.I. = 95% = 0.95% = 1 – 0.95 = 0.05/2 t = 0.025

p(100 – p) n

δp = 60(100 – 60) 20 δp =

2400 20

δp = √120

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δp = 10.9% With a confidence level of 95 percent, the t value = 2.093. There fore, the interval estimate is = p – t δp <

< p+ t δp

= 60 – (2.093) (10.9) < = 37.18 <

< 60 + (2.093) (10.9)

< 82.8 percent

So we can be 95 percent confident that the true percentage of PAF KIET girls who are satisfied is between 37.18 and 82.8 percent. DISCUSSION AND INTERPRETATION From the facts and figures we have calculated in the previous section, it is evident that we can be 90% confident that boys are satisfied between the range of 25.77 and 64.22 percent and the rest are dissatisfied. Whereas we can be 95% confident that girls are satisfied between the range of 37.18 and 82.8 percent and the remaining are dissatisfied. Hence, we have worked out the population percentage of students who are satisfied with the transportation service provided by PAF KIET INSTITUTE which will help us come up with a recommendation for the management to improve their services for those students who are dissatisfied.

CONCLUSION AND RECOMMENDATION Therefore, we conclude that the transport management should arrange more points to satisfy 55% of the boys and 40% 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 the students 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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