Statistics Inference project final

STATISTICS & INFERENCE REPORT

Analysis on Reliable ISP in Karachi

Submitted To : M.SHAHBAZ KHAN

Class ID : 53965

Submitted By : MUHAMMAD OSAMA (53234) SYED ADNAN SHAH (53218)

USMAN GHANI (53007) SAQIB SHAIKH (53044)

of 22

TABLE OF CONTENTS

Acknowledgment 03

Nature & background 04

Objective 05

Confidence interval for a proportion 09

Hypothesis testing for average used of Internet in a day 15

Correlation between age of user with Price of Internet 11

Goodness of fit Test 19

Conclusion 22

of 22

ACKNOWLEDGEMENT

A project of this nature and magnitude was a very good learning

experience. We owe a debt of gratitude to those people who aided us in the

compilation of this project.

Firstly we thank Almighty ALLAH for giving us the strength to compile this

report. We take this opportunity to thank our valued instructor “SIR

SHABAZ KHAN” for giving us the opportunity to conduct a study of this

nature for the course of “STATISTICS & INFERENCE”.

of 22

NATURE & BACKGROUND OF STUDY

A computer network consisting of a worldwide network of computer networks that

use network protocols to facilitate data transmission called ‘Internet’. The

companies who are providing this service called “Internet Services Provider (ISP).

In 1996, Brain net introduced internet first time in Pakistan through Dial-up

connection.

There are four types of internet connection in Karachi, i.e. i.e. Dial-up, Cable net,

Wimax and DSL (Digital Subscriber Line). Wimax and DSL are new technologies

that offer fast speed as compared to dialup and cable net.

There are many ISP’s available in Karachi but here we are focusing only on three

companies, i.e. PTCL, WORLDCALL and WATEEN.

PTCL is offering two types of Internet connection, i.e. Dial-up and DSL. WATEEN

is offering Wimax and DSL connection and WORLDCALL is offering Cable Net and

DSL connection.

of 22

OBJECTIVE

STUDY ABOUT THE RELIABLE INTERNET SERVICE PROVIDER (ISP)STUDY ABOUT THE RELIABLE INTERNET SERVICE PROVIDER (ISP)

IN KARACHIIN KARACHI

RELIABILITY means the ability of a person or system to perform and maintain its

functions in routine circumstances, as well as hostile or unexpected circumstances. Its

depend on many factors. For ISP company, its depend on:

Goodwill of the company in the market,

Fast speed of internet at low/ affordable charges with consistent connectivity

and satisfied customer services, etc.

For our study we have asked Ten (10) Questions related to user choices, preferences

and facilities which they often demand from any ISP. Following are the Questions

which help us to identify the most Reliable ISP.

1) Gender

2) Age

3) If you have an offer to get DSL (or Internet) connection, which company

connection would you prefer ?

4) How much Speed you will prefer?

5) How much maximum amount would you like to pay?

6) Which type payment mode would you like to pay (post pay or prepay)

7) How many hours you use internet in a week?

8) How many computers or devices would you like to use?

9) Would you like to recommend your DSL connection to others?

10) Are you satisfy with customer support services?

of 22

SAMPLE DATA

S.NO. Q 1. Q 2. Q 3. Q 6. Q 7. Q 8. Q 9. Q 10.

1 MALE 28 PTCL 1 MB Rs. 1,200 Postpay 20 2 Yes Yes

2 FEMALE 21 PTCL 1 MB Rs. 840 Postpay 25 1 Yes Yes

3 MALE 25 WORLDCALL 1 MB Rs. 1,800 Postpay 30 1 No No

4 FEMALE 22 WORLDCALL 2 MB Rs. 2,400 Prepay 20 3 No No

5 MALE 18 PTCL 1 MB Rs. 840 Postpay 21 1 Yes Yes

6 FEMALE 19 WORLDCALL 1 MB Rs. 1,800 Postpay 22 1 Yes Yes

7 FEMALE 26 PTCL 1 MB Rs. 1,200 Postpay 20 2 Yes Yes

8 MALE 25 WORLDCALL 1 MB Rs. 1,800 Postpay 19 1 No No

9 FEMALE 22 WATEEN 2 MB Rs. 1,500 Prepay 30 3 Yes Yes


11 MALE 20 WATEEN 2 MB Rs. 1,500 Prepay 29 2 No No

12 FEMALE 18 PTCL 2 MB Rs. 1,400 Postpay 35 2 No No

13 MALE 18 WATEEN 1 MB Rs. 799 Postpay 25 1 Yes Yes


15 MALE 28 WATEEN 2 MB Rs. 799 Prepay 22 1 Yes Yes


17 MALE 22 WATEEN 1 MB Rs. 799 Postpay 24 1 No No


19 FEMALE 20 WATEEN 1 MB Rs. 799 Prepay 24 1 Yes Yes

20 MALE 18 WATEEN 2 MB Rs. 1,500 Prepay 30 3 Yes Yes




24 MALE 24 PTCL 1 MB Rs. 840 Prepay 24 1 Yes Yes





29 MALE 19 WORLDCALL 1 MB Rs. 1,800 Prepay 22 1 No Yes

30 FEMALE 19 WORLDCALL 2 MB Rs. 1,400 Prepay 21 1 Yes Yes

31 MALE 27 PTCL 1 MB Rs. 840 Postpay 34 2 No Yes

32 FEMALE 22 PTCL 1 MB Rs. 840 Postpay 18 2 No No



35 MALE 19 PTCL 1 MB Rs. 840 Postpay 21 3 No No

36 MALE 23 PTCL 2 MB Rs. 1,400 Postpay 25 3 Yes No



39 FEMALE 21 PTCL 2 MB Rs. 1,400 Postpay 26 1 Yes No


41 FEMALE 26 WORLDCALL 2 MB Rs. 1,400 Prepay 30 3 Yes Yes

42 MALE 22 WORLDCALL 1 MB Rs. 1,800 Prepay 25 2 No No

43 MALE 18 WORLDCALL 1 MB Rs. 1,800 Prepay 34 2 Yes Yes

44 MALE 19 PTCL 2 MB Rs. 1,400 Postpay 41 4 No No


Q 4. Q 5.

of 22

S.NO. Q 1. Q 2. Q 3. Q 6. Q 7. Q 8. Q 9. Q 10.



48 FEMALE 23 WORLDCALL 2 MB Rs. 1,400 Prepay 10 1 No Yes


50 FEMALE 20 WATEEN 2 MB Rs. 1,000 Postpay 15 1 No Yes

51 FEMALE 19 WATEEN 1 MB Rs. 800 Postpay 16 2 Yes No


53 MALE 30 PTCL 2 MB Rs. 1,500 Prepay 30 3 No Yes



56 MALE 25 PTCL 1 MB Rs. 999 Prepay 29 2 No No



59 MALE 23 WATEEN 2 MB Rs. 1,000 Postpay 21 1 Yes Yes

60 MALE 22 WATEEN 1 MB Rs. 800 Prepay 25 1 Yes No


62 MALE 21 WORLDCALL 2 MB Rs. 1,400 Prepay 10 1 No No


64 MALE 22 WATEEN 1 MB Rs. 1,500 Prepay 28 2 Yes Yes



67 MALE 24 PTCL 2 MB Rs. 840 Prepay 28 1 No No

68 MALE 22 PTCL 2 MB Rs. 1,900 Postpay 21 1 No No


70 FEMALE 23 WATEEN 1 MB Rs. 799 Prepay 21 1 No No



73 MALE 21 WORLDCALL 2 MB Rs. 1,800 Postpay 35 1 Yes Yes

74 MALE 25 WATEEN 2 MB Rs. 799 Postpay 28 2 No No



77 FEMALE 24 PTCL 2 MB Rs. 840 Prepay 20 2 Yes Yes




Q 4. Q 5.

of 22

PTCL

67%

33%

Male Female

WATEEN

70%

30%

Male Female

WORLDCALL

50%50%

Male Female

SUMMARY OF SAMPLE DATA

Company Male Female Total Relative %age Mean Median Variance Standard

deviatioon Minimum Maximum

PTCL 29 14 43 53.75% 1,055 840 95,322 309 840 1,999 WATEEN 16 7 23 28.75% 939 799 72,655 270 799 1,500 WORLDCALL 7 7 14 17.50% 1,700 1,800 78,462 280 1,400 2,400

52 28 80

of 22

CONFIDENCE OF INTERVAL FOR PROPORTION

Objective

To construct a 95% Confidence Interval of population proportion of users who are using internet connection of PTCL, Worldcall and Wateen respectively.

Data and Sample Size

The data is primary and has been collected through survey in facebook. A sample of 80 individuals’ was taken.

Sampling technique

The sampling technique that was used in the survey is Convenience Sampling. We have used sample data from Question 5.

of 22

Statistical Method

We have applied Confidence interval for a population proportion at 95% level of confidence interval.

Data:

Variable No. of user Relative ratio

PTCL 43 0.5375WORLDCALL 14 0.175WATEEN 23 0.2875

Sampe Size, n = 80

Z value = 1.96

Formula

Calculation

( 0.5375 ) + ( 1.960) (0.5375) ( 1 - 05375 ) ( 0.175 ) + ( 1.960) ( 0.175 ) (1 - 0.175 )80 80

PTCL WORLDCALL

0.428 < p < 0.6465 0.0917 < p < 0.2582

( 0.2875 ) + ( 1.960) ( 0.2875 ) (1 - 0.2875 )80

WATEEN

0.18832 < p < 0.386

Conclusion

Hence with 95% confidence the true percentage of internet users of PTCL is 42.18%

to 64.65%, Worldcall is 9.17 % to 25.82% and Wateen is 18.83% to 38.6% in Karachi.

of 22

CORRELATION & REGRESSION

Objective

The objective of this test is to determine the fact that there a significant relationship between the age of users and the price of internet charged by ISP.

Population

Internet Subscriber Sample Size, Data

The sample size was of 80 observations. The data was primary.

Sampling Technique

The sampling technique used was convenience sampling. We have used sample data from Question 2 & 5. We have used Q2. as an Independent variable (x) and Q 5 as dependent variable (y).

Statistical method

The method we have used is Correlation Hypothesis Testing.

of 22

Problem

The research has been conducted to determine whether there is a relationship between the age of internet user and the price / charges of internet. Data

Sample size: n = 80 , ∞ = 0.05 , Test: Two tailed test.

Step 1

Ho: There is no correlation between the age of internet user and the price charge by ISP

HA: There is a correlation between the age of internet user and the price charge by ISP (claim).

Step 2

Since ∞ = 0.05 and degree of freedom is 80 - 2 = 78, the critical values obtained from Table F are +- 1.960. r represent coefficient of correlation and r2 represent Coefficient of determination.

Step 3

Statistical Methods

Co-Relation

r = ( 80 ) ( 2,029,717) - ( 1,807) ( 89,988)

[ (80)(41,499) - ( 1,807)2 ] [ (80) ( 113,260,222) - ( 89,988)2 ]

r = - 0.0318 r2 = 0.0010131 or 0.10%

Test is not significant. Calculation of regression is meaningless

of 22

T Calculation

Step 4

Decision Rule

Step 5: Conclusion

T- Cal lies in the acceptance region so we accept Ho (null hypothesis).

There is no correlation between the age of internet users and the price of internet charged by ISPs’.

of 22

Scatter Diagram

500

700

900

1100

1300

1500

1700

1900

2100

2300

2500

15 17 19 21 23 25 27 29 31 33 35

GENDER

PRICE

of 22

-1.96

HYPOTHESIS TESTING

Objective

The objective of this test is to find out the average used of internet (in hrs) in a day by Karachi users.

Population

Internet subscriber

Sample Size, Data:

The sample size is 80 observations consist of (PTCL 43, Wateen 23, Worldcall 14) respectively. The data is primary. We have used sample data from Question 7.

Sampling Technique

Convenience sampling has been used

Statistical method:

The method we have used is Hypothesis Testing.

of 22

Problem

The researcher claims that the average used of internet in Karachi is 3 hours in a day To test the claim, Is there enough evidence to reject the claim at ∞=0.05.

Sample size is 80 observations consist of PTCL 43, Wateen 23, Worldcall 14 respectively.

Source:

http://www.dawn.com/wps/wcm/connect/dawn-content-library/dawn/news/pakistan/03-all-resources-to-be-used-for-power-generation-ss-10?pageDesign=Advertise_DAWN

Data

PTCL WORDLCALL WATEEN

Sample Size ( n ) 43 14 23Mean ( X ) 3.52 hrs 3.19 hrs 3.66 hrsStandard deviation ( s ) 0.957 1.316 1.25Mean (μ) 3 hrs 3 hrs 3 hrs

Test: Two tailed test.

Step 1

Ho : The average used of internet in Karachi is 3 hrs in a day. (claim)

HA : The average used of internet in Karachi is not 3 hrs in a day.

Step 2

Since ∞ = 0.05 and critical values are +- 1.960 ( PTCL) , +-2.145 ( Worldcall) and +- 2.069 (Wateen).

Step 3

Formula :

** When n < 30 , t distribution would be used instead of z. The formula would changed to ‘ t ’.

of 22

Calculation:

z = 3.52 - 3 t = 3.19 - 3 0.957 1.316

43 14

z = 3.563 t = 0.540

Accept HoReject Ho

PTCL WORLDCALL

t = 3.66 - 3 1.2523

t = 2.532

WATEEN

Reject Ho

Step 4

Decision Rule: Two tailed test

of 22

-1.96

Step 5: Conclusion

For PTCL and Wateen

Since Z cal value lies in the rejection region, hence reject Ho and accept HA. Now we

can say that average used of internet in Karachi is not 3 hrs in a day.

For Worldcall

Since Z cal value lies in the acceptance region, hence accept Ho and reject H A. Now

we can say that average used of internet in Karachi is 3 hrs in a day.

of 22

GOODNESS OF FIT TEST

Objective

To see whether a frequency distribution fits a specific pattern

Population

Internet subscriber

Sample Size, Data:

The sample size is 80 observations. The data is primary. We have used sample data from Question 3 and 10.

Sampling Technique

Convenience sampling has been used

Data

CLAIM

A CEO of Internet company wishes to know that whether customers show any preference while selecting Internet Service Provider (ISP)?. The samples of 80 observations were taken from Question 3 and 10 and let Alpha value is 0.05.

PTCL WATEEN WORLDCALL

No. of subscriber 43 23 14

of 22

Solution

Step 1

State the hypotheses:

Ho : Customers show no preference while selecting Internet Service Provider (ISP)

HA : Customers show preference while selecting Internet Service Provider (ISP) (Claim)

If there were no preference, one would expect each frequency to be selected with equal frequency. In this case 80/4 = 26.666

PTCL WATEEN WORLDCALL

Observed value 43 23 14

Expected value 26.66 26.66 26.66

Step 2

Find the critical value. The degree of freedom are (c-1) = 3 - 1 = 2 and the critical value from table G is = 5.991 at alpha is 0.05.

Step 3

Compute the test value by subtracting the expected value from the observed value, Squaring the result and dividing by the expected value, and finding the sum. The expected value for each category is 26.66.

Formula for test value:

X2 = (O – E) 2 E

X2 = (43 – 26.66)2 + ( 23 – 26.66) 2 + ( 14 – 26.66) 2

26.66 26.66 26.66 = 16.529

of 22

Step 4

GRAPH Right - Tailed - Test

Make the decision. The decision is to reject null hypothesis, since

16.5291 > 5.991

Step 5

CONCLUSION

The value lies in rejection region so reject Ho and accept HA, it can be concluded that Customers show preference while selecting Internet Service Provider. So Test is “Not a good fit”.

of 22

CONCLUSION

“ We can say PTCL is a most reliable ISP in Karachi ”

Because the company is offering some unique services as compared to

competitors. Like DSL, Smart TV and Land line in ONE connection and also

offering fast internet speed with consistent connectivity and also maintaining

satisfied customer services. The most important benefit for student is 30%

reduction on internet charges.

of 22

Statistics Inference project final

Documents

Transcript of Statistics Inference project final