Chapter 12 Statistical Inference: Other One-Sample Test Statistics
Statistics Inference project final
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Transcript of 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)
Page 1 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
Page 2 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”.
Page 3 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.
Page 4 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?
Page 5 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
10 MALE 19 PTCL 1 MB Rs. 1,200 Postpay 18 2 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
14 FEMALE 22 PTCL 1 MB Rs. 840 Postpay 21 1 Yes Yes
15 MALE 28 WATEEN 2 MB Rs. 799 Prepay 22 1 Yes Yes
16 MALE 24 PTCL 1 MB Rs. 840 Postpay 25 1 Yes Yes
17 MALE 22 WATEEN 1 MB Rs. 799 Postpay 24 1 No No
18 FEMALE 19 PTCL 1 MB Rs. 1,200 Postpay 25 3 Yes Yes
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
21 FEMALE 18 PTCL 1 MB Rs. 840 Postpay 19 1 Yes Yes
22 MALE 22 PTCL 1 MB Rs. 840 Postpay 18 1 Yes Yes
23 MALE 25 WATEEN 1 MB Rs. 799 Prepay 30 1 Yes Yes
24 MALE 24 PTCL 1 MB Rs. 840 Prepay 24 1 Yes Yes
25 MALE 22 WATEEN 1 MB Rs. 799 Postpay 20 1 Yes Yes
26 FEMALE 19 PTCL 1 MB Rs. 840 Postpay 21 1 Yes Yes
27 FEMALE 24 PTCL 1 MB Rs. 840 Postpay 12 1 Yes Yes
28 MALE 21 PTCL 2 MB Rs. 1,400 Postpay 23 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
33 FEMALE 19 WATEEN 2 MB Rs. 799 Prepay 24 2 Yes Yes
34 MALE 25 WATEEN 1 MB Rs. 799 Prepay 54 3 Yes Yes
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
37 MALE 22 WATEEN 1 MB Rs. 799 Prepay 44 3 Yes Yes
38 MALE 24 PTCL 1 MB Rs. 840 Postpay 32 1 No Yes
39 FEMALE 21 PTCL 2 MB Rs. 1,400 Postpay 26 1 Yes No
40 FEMALE 27 PTCL 1 MB Rs. 840 Postpay 30 1 Yes Yes
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
45 MALE 20 PTCL 1 MB Rs. 840 Postpay 39 2 Yes Yes
Q 4. Q 5.
Page 6 of 22
S.NO. Q 1. Q 2. Q 3. Q 6. Q 7. Q 8. Q 9. Q 10.
46 FEMALE 28 PTCL 2 MB Rs. 1,500 Postpay 15 1 Yes Yes
47 FEMALE 26 PTCL 2 MB Rs. 1,500 Postpay 18 1 Yes Yes
48 FEMALE 23 WORLDCALL 2 MB Rs. 1,400 Prepay 10 1 No Yes
49 FEMALE 21 WORLDCALL 2 MB Rs. 1,400 Postpay 5 2 Yes 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
52 FEMALE 19 WATEEN 1 MB Rs. 800 Prepay 16 1 Yes Yes
53 MALE 30 PTCL 2 MB Rs. 1,500 Prepay 30 3 No Yes
54 MALE 29 PTCL 1 MB Rs. 999 Prepay 24 1 Yes Yes
55 MALE 25 PTCL 1 MB Rs. 999 Prepay 12 2 Yes Yes
56 MALE 25 PTCL 1 MB Rs. 999 Prepay 29 2 No No
57 MALE 24 PTCL 1 MB Rs. 999 Postpay 30 3 Yes Yes
58 MALE 24 PTCL 1 MB Rs. 999 Postpay 35 2 No Yes
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
61 MALE 22 WATEEN 1 MB Rs. 800 Postpay 20 2 Yes Yes
62 MALE 21 WORLDCALL 2 MB Rs. 1,400 Prepay 10 1 No No
63 MALE 22 PTCL 1 MB Rs. 840 Postpay 21 1 Yes Yes
64 MALE 22 WATEEN 1 MB Rs. 1,500 Prepay 28 2 Yes Yes
65 MALE 25 PTCL 2 MB Rs. 840 Prepay 24 1 Yes Yes
66 FEMALE 24 WORLDCALL 1 MB Rs. 1,800 Postpay 30 1 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
69 MALE 21 WATEEN 1 MB Rs. 799 Postpay 22 1 Yes Yes
70 FEMALE 23 WATEEN 1 MB Rs. 799 Prepay 21 1 No No
71 MALE 25 PTCL 1 MB Rs. 840 Prepay 28 1 Yes Yes
72 MALE 24 PTCL 1 MB Rs. 840 Prepay 28 1 Yes Yes
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
75 MALE 24 WATEEN 1 MB Rs. 799 Postpay 21 1 Yes Yes
76 MALE 26 PTCL 1 MB Rs. 840 Prepay 35 2 Yes Yes
77 FEMALE 24 PTCL 2 MB Rs. 840 Prepay 20 2 Yes Yes
78 MALE 27 PTCL 2 MB Rs. 1,999 Postpay 28 1 Yes Yes
79 MALE 22 PTCL 1 MB Rs. 840 Prepay 21 1 Yes Yes
80 MALE 24 PTCL 1 MB Rs. 840 Prepay 21 1 Yes Yes
Q 4. Q 5.
Page 7 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
Page 8 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.
Page 9 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.
Page 10 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.
Page 11 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
Page 12 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’.
Page 13 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
Page 14 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.
Page 15 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 ’.
Page 16 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
Page 17 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.
Page 18 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
Page 19 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
Page 20 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”.
Page 21 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.
Page 22 of 22