This PPT deals with the problems and solutions for sampling of large variables and relate, compare the observations with the exception of the population sample ie testing the difference between means of two samples, standard error of the difference between two standard deviations.
OpenGL Mini Projects With Source Code [ Computer Graphics ] WITH SOURCE CODES
Paid OpenGL projects • Here’s about 30+ OpenGL GLUT projects. • Price $5 • Easy Payment methods: For Bangladesh and other Countries .
If you are interested to get these projects, just mail the project name along with your name, and institute name. I’ll Contact You As Soon As Possible .
EMAIL:- k4nc80n@gmail.com
FACEBOOK:- https://www.facebook.com/k4nc80n
Source Code :- k4nc80n@gmail.com
For more Project :-
EMAIL:- k4nc80n@gmail.com
FACEBOOK:- https://www.facebook.com/k4nc80n
INSTAGRAM:- https://www.instagram.com/k4nc80n
TWITTER:- https://www.twitter.com/K4NC80N
This PPT deals with the problems and solutions for sampling of large variables and relate, compare the observations with the exception of the population sample ie testing the difference between means of two samples, standard error of the difference between two standard deviations.
OpenGL Mini Projects With Source Code [ Computer Graphics ] WITH SOURCE CODES
Paid OpenGL projects • Here’s about 30+ OpenGL GLUT projects. • Price $5 • Easy Payment methods: For Bangladesh and other Countries .
If you are interested to get these projects, just mail the project name along with your name, and institute name. I’ll Contact You As Soon As Possible .
EMAIL:- k4nc80n@gmail.com
FACEBOOK:- https://www.facebook.com/k4nc80n
Source Code :- k4nc80n@gmail.com
For more Project :-
EMAIL:- k4nc80n@gmail.com
FACEBOOK:- https://www.facebook.com/k4nc80n
INSTAGRAM:- https://www.instagram.com/k4nc80n
TWITTER:- https://www.twitter.com/K4NC80N
This is a project documentation titled: Online Railway Reservation System.
This documentation was submitted by me as my assignment in my 6th sem (2013) in APIIT SD INDIA, Panipat along with a full-fledged working system i.e., a website built using ASP.NET & SQL SERVER 2008
Collision prevention on computer architectureSarvesh Verma
Download From:-
http://www.linkshrink.net/7L1GbM
Collision Prevention on Computer Architecture in this topic we are cover latency,reservation table,collision vector,etc.
This project is about ' ONLINE RAILWAY RESERVATION SYSTEM ' that automates the process of generating tickets to the passengers. This System allows passengers to view Trains and Available seats(options like Berth availability , class are also included) , view , book & cancel the tickets online.
Resume and CV Summarization using NLP Reportsneha indulkar
This project proposes a model of extracting important information from the semi-structured
text format in a curriculum vitae or resume and ranking it according to the preference of the
associated company and requirements. In order to achieve the desired goal, the entire process has
been divided into 3 basic segments. The first segment consists of segmenting the entire CV /
Resume based on the topic of each part, the second segment consists of extracting data in
structured form from the unstructured data and the final segment consists of evaluating the
structured data by decision tree algorithm and training the system. The structured data extraction
process is done by segmenting the entire CV / Resume by converting it to text. After the
conversion to structured data, decision tree algorithm techniques are used to classify the input into
different categories based on qualifications, experience, etc.
This is a project documentation titled: Online Railway Reservation System.
This documentation was submitted by me as my assignment in my 6th sem (2013) in APIIT SD INDIA, Panipat along with a full-fledged working system i.e., a website built using ASP.NET & SQL SERVER 2008
Collision prevention on computer architectureSarvesh Verma
Download From:-
http://www.linkshrink.net/7L1GbM
Collision Prevention on Computer Architecture in this topic we are cover latency,reservation table,collision vector,etc.
This project is about ' ONLINE RAILWAY RESERVATION SYSTEM ' that automates the process of generating tickets to the passengers. This System allows passengers to view Trains and Available seats(options like Berth availability , class are also included) , view , book & cancel the tickets online.
Resume and CV Summarization using NLP Reportsneha indulkar
This project proposes a model of extracting important information from the semi-structured
text format in a curriculum vitae or resume and ranking it according to the preference of the
associated company and requirements. In order to achieve the desired goal, the entire process has
been divided into 3 basic segments. The first segment consists of segmenting the entire CV /
Resume based on the topic of each part, the second segment consists of extracting data in
structured form from the unstructured data and the final segment consists of evaluating the
structured data by decision tree algorithm and training the system. The structured data extraction
process is done by segmenting the entire CV / Resume by converting it to text. After the
conversion to structured data, decision tree algorithm techniques are used to classify the input into
different categories based on qualifications, experience, etc.
You are to select an appropriate organisation that you have access to. This will most likely be the organization that you currently work for. The organization may be a private, a public or a voluntary organization. You may want to focus on a unit, sub division or even a department within the organization, particularly if the organization is very large or operates on an international or global scale. You may disguise the real identity of the organization by using a fictitious name if you prefer.
Risk management of telecommunication and engineering laboratorySalam Shah
The Telecommunication laboratory plays an important role in carrying out research in the different fields like Telecommunication, Information Technology, Wireless Sensor Networks, Mobile Networks and many other fields. Every Engineering University has a setup of laboratories for students particularly for Ph.D. scholars to work on the performance analysis of different Telecommunication Networks including WLANs, 3G/4G, and Long Term Evolution (LTE). The laboratories help students to have hand on practice on the theoretical concepts they have learned during the teachings at the university. The technical subjects have a practical part also which boosts the knowledge of students and learning of new ideas. The Telecommunication and Engineering laboratories are equipped with different electronic equipment’s like digital trainers, simulators etc. and some additional supportive devices like computers, air conditioners, projectors, and large screens, with power backup facility that creates the perfect environment for experimentation. The setup of Telecommunication and Engineering laboratories cost huge amount, required to purchase equipment, and maintain the equipment. In any working environment risk factor is involved. To handle and avoid risks there must be risk management policy to tackle with accidents and other damages during working in the laboratory, may it be human or equipment at risk. In this paper, we have proposed a risk management policy for the Telecommunication and Engineering laboratories, which can be generalized for similar type of laboratories in engineering fields of studies.
Supermarket by Trueventus is the latest addition to the signature shopping mall event. This event is crafted uniquely for the grocery, supermarket and FMCG retail players for unparalleled opportunities to learn, engage, share, network, and innovate. Given today’s ever-changing marketplace and evolving advancements in innovation for the grocery industry, this is truly a not-to-miss event! EVENT HIGHLIGHT includes Interactive panel discussion, Best practice and case study sharing,Features latest innovative and game-changing products and solutions,Obtain ideas to drive profitable growth to your company,Optimise business relationships between peers and industry players,One to one meeting with shopping mall & retail industry players.
For registration/inquiry, please contact:
Corin Tan
Project Manager - Marketing
Tel: +603-2775 0000 (ext 510)
Email: corint@trueventus.com
Full paper technologies and strategies for providing education through (july 14)Isdianto Isdianto
As we know that technology helps many people in the world whatever their fields. One of the main benefit of the technology is the helping distance teaching and learning. Technology here is the main support for the educational development in the most remote regions in Indonesia. Many people use the advanced technologies, such as internet, as the main wares of the educational development. They promote the using of internet in many schools in Indonesia, specially in remote regions, such as remote regions in Sumatera, Kalimantan, Sulawesi and Papua. Today, most of the students in such remote regions always have fun in their study with internet as the advanced technology. Technology has enchaned teaching and learning method in Indonesia, Specially in remote region. Many Students has used advanced technology, such as computer in the classroom, new website, interactive key board, Blog and wikis, in this case, Web 2.0 that implemented in the class, so the students can have much more dialogues, digest dialogues, ideas and brainstorming. Beside that kinds, wireless michrophone, mobile and digital game, also to be the other alternatives of the advanced technologies in enchanced teaching and learning system. Distance educational system by using advanced technologies make the goal of international education system become more achievable and more accessible to all students. Here, Technology has more contributions to the enchanced teaching and learning system, like what display in this site: http://www.slideshare.net/NASuprawoto/penggunaan-internet-dalam-pembelajaran-matematika-di-sd. This research is using desciptive methode for describing much more about strategies for providing education at remote area, west kalimantan, such as Open and Distance Learning System and getting sample at Open Distance Learning of Pontianak, West Kalimantan.
Here, Online tutorial is the most favourable mechanism for providing education through Open and Distance Learning System all over the world. Online tutorial gives the students so many things and choices for learning, beginning from the materials of studies, the choices of books shopping, various literatures at online library, various kind of friends for communicating between one student to another.
So, Technologies and Online Learning Strategies can provide education through Open and Distance Learning System at Remote Regions in Indonesia.
Key words : Technologies, Strategies, education, Open and Distance Learning System, Remote
Area
This was a 2 month project for a major telecommunication company. This is merely a high-level overview of the work completed, but will give the reader an idea of the process (without divulging proprietary and confidential information).
This powerpoint presentation was done as part of the course STAT 591 titled Mater's Seminar during Third semester of MSc. Agricultural Statistics at Agricultural College, Bapatla under ANGRAU, Andhra Pradesh.
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
This lecture is based on post-graduate medical students of all subject those who are students MS/MD/FCPS of different subject on Central Tendency and Dispersion.
Final Project ScenarioA researcher has administered an anxiety.docxAKHIL969626
Final Project Scenario
A researcher has administered an anxiety survey to students enrolled in graduate level statistics courses. The survey included three subscales related to statistics anxiety: (a) interpretation anxiety, (b) test anxiety, and (c) fear of asking for help. For the items that comprised the scales, students were asked to respond using a 5 point likert-type scale ranging from (1) No Anxiety to (5) High Anxiety. Therefore, higher scores on the anxiety subscales implied higher levels of anxiety.
In addition to the statistics anxiety subscales, the survey contained a subscale related to the use of statistical software and a subscale related to self-perceived confidence concerning general computer use. Students responded to items on the statistical software subscale using a response range from (1) Strongly Disagree to (7) Strongly Agree. For the computer confidence subscale, students responded to items using a range from (1) Strongly Disagree to (5) Strongly Agree. For each of these subscales, higher scores implied higher levels of confidence.
The researcher determined the score for each subscale by computing the mean response for the items associated with the subscale. This technique resulted in subscales that had the same possible range and the items that made up the subscale.
A subsample of the researcher’s dataset contains the following variables that should be used for completing the four final projects. The variables included in the dataset are:
Variable name:
Label:
Values:
gender
1: Female
2: Male
race
1: White
2: Non-White
age
courses
Number of online courses completed
1: 0-2 courses
2: 3-7 courses
3: 8 or more courses
interpret
Anxiety associated with reading and interpreting output from analyses
test
Anxiety associated with taking a test in a statistics course
help
Anxiety associated with asking for help during a statistics course
software
Self-reported level of confidence is using statistical software
computer
Self-reported confidence in general computer use
Final Project 1:
Use SPSS to conduct the necessary analysis of the Age variable and answer each of the following questions.
Questions:
1. What is the value of n?
2. What is the mean age?
3. What is the median age?
4. What was the youngest age?
5. What was the oldest age?
6. What is the range of ages?
7. What is the standard deviation of the ages?
8. What is the value of the skewness statistic?
9. What are the values of the 25th, 50th, and 75th percentiles?
10. Present the results as they might appear in an article. This must include a table and narrative statement that provides a thorough description of the central tendency and distribution of the ages.
Final Project 2
One of the researcher’s questions involved the difference in scores on the Interpretation Anxiety subscale between male and female respondents. Use SPSS to conduct the analysis that is appropriate for this research question and answer each o ...
OWA BASED MAGDM TECHNIQUE IN EVALUATING DIAGNOSTIC LABORATORY UNDER FUZZY ENV...ijfls
The aim of this paper is to present an evaluation process using OWA operator in fuzzy Multi-attribute
group decision making (MAGDM) technique for helping the health-care department to choose a suitable
diagnostic laboratory among several alternatives. In the process of decision making, experts provide
linguistic terms to evaluate each of the alternatives, which are parameterized by generalized triangular
fuzzy numbers (GTFNs). Subsequently fuzzy MAGDM method is applied to determine the overall
performance value for each alternative (laboratory) to make a final decision. Finally, the diagnostic
laboratory evaluation problem is presented involving seven evaluation attributes, five laboratories and five
experts.
Math 221 Massive Success / snaptutorial.comStephenson164
1. (TCO 1) An Input Area (as it applies to Excel 2010) is defined as______.
2. (TCO 1) In Excel 2010, a sheet tab ________.
3. (TCO 1) Which of the following best describes the AutoComplete function?
4. (TCO 1) Which of the following best describes the order of precedence as it applies to math operations in Excel?
UNIT 3
SUCCESS GUIDE
1 | GB 513 Unit 3 Success Guide v.6.13.17
UNIT 3 SUCCESS GUIDE
This unit is the other “most difficult” one. Hypothesis testing has two parts: setting-up
the hypotheses and calculating the critical values to determine results. They both
pose difficulty for a lot of students. The seminar will be on the first and the recorded
lecture will be on the second. You need to make sure you understand both,
otherwise you will not be able to get to the right conclusions.
1. As always, start by reading the chapters and studying the solved examples.
2. Watch the lecture video in document sharing. It focuses on why we do
hypothesis testing, how to do it with Excel and solves two sample problems.
3. Watch this from Khan Academy:
https://www.khanacademy.org/math/statistics-probability/significance-
tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-
values
This one talks more about how to write the null and alternative hypotheses
(which a lot of students get wrong) and also solves the problem using
formulas.
4. Watch the sample problem solutions in Course Resources.
5. If you still want more videos, search YouTube for “hypothesis testing.” Several
introductory level videos are available, such as
https://www.youtube.com/watch?v=HmMjS88eSVE and
https://www.youtube.com/watch?v=0zZYBALbZgg
Email your instructor if you find any of these links to be broken.
Avoid these mistakes!
GENERAL NOTES
RESOURCES
COMMON MISTAKES IN THE ASSIGNMENT
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=0zZYBALbZgg
http://www.youtube.com/watch?v=0zZYBALbZgg
http://www.youtube.com/watch?v=0zZYBALbZgg
2 | GB 513 Unit 3 Success Guide v.6.13.17
Students commonly get the null and alternative hypotheses reversed, or
get them completely wrong.
Students also commonly do not state the hypothesis fully. This is correct:
“null hypothesis: there is no difference between the average salary for
group 1 and the average salary of group 2.” This is not sufficient: “ho:
x1=x2”
Students sometimes compare the averages of the two groups and base
their determination on which one is greater, rather than properly doing a
hypothesis test.
Students sometimes do the calculations correctly, but do not write out
what the conclusion is. This is correct: “We therefore reject the null
hypothesis, which means we conclude that there i ...
Sequence-to-Sequence Modeling for Time SeriesArun Kejariwal
In this talk we overview Sequence-2-Sequence (S2S) and explore its early use cases. We walk the audience through how to leverage S2S modeling for several use cases, particularly with regard to real-time anomaly detection and forecasting.
Similar to Case study: Probability and Statistic (20)
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Tutorial for 16S rRNA Gene Analysis with QIIME2.pdf
Case study: Probability and Statistic
1. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
1
Assignment Content
I. PURPOSE OF SURVEY....................................................................................................2
1. Objective.........................................................................................................................2
2. Domain: (ITC students from year 1 to year 5.)...............................................................2
3. Data.................................................................................................................................2
II. ANALYSIS OF DATA ......................................................................................................3
1. THEORY AND ASSUMPTION....................................................................................3
2. TEST HYPOTHESIS AND CONFIDENCE INTERVAL CONDUCTING.................4
III. STATISTICAL ANALYSIS ..........................................................................................5
a) For students in year 𝟏:.................................................................................................5
b) For students in year 2:.................................................................................................6
c) For students in year 3:.................................................................................................7
d) For students in year 4:.................................................................................................7
e) For students in year 5:.................................................................................................8
f) For entire students in ITC: ..........................................................................................8
IV. CONCLUSION...............................................................................................................9
3. Our interest in this case study:........................................................................................9
2. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
2
I. PURPOSE OF SURVEY
1. Objective
We decided to conduct this survey in order to estimate the percentage of students in
ITC using smartphone in various models especially iPhone.
We aim to use the result from this survey to:
Estimate the true proportion of students in ITC using some smartphone models from
year 1 to 5 as well as the entire institute.
Estimate the tendency of ITC’s students in using smartphones from first year to fifth
year
Conduct the hypothesis whether or not the true proportion of students using iPhone in
each year and all students in ITC exceed 50%?
2. Domain: (ITC students from year 1 to year 5.)
3. Data
The data are collected by surveying directly with the students (Survey sheet) and
doing online (Online survey sheet).
Case Study: The Telephone Preference in Institute of Technology of Cambodia
3. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
3
Problems:
In order to know the preference of the student in ITC in using Smartphone, we decided to do
a survey among 307 students from year 1st
to year 5th
randomly. After surveying, the results
showed that the numbers of students who use iPhone, Samsung, Nokia, Sony and other
models is respectively listed as the table below.
Data of students using different phones models
Phone Type
Students
iPhone Samsung Nokia Sony other Total
Year 1 52 18 5 0 7 82
Year 2 45 14 7 4 6 76
Year 3 35 13 6 1 6 61
Year 4 33 6 5 2 5 51
Year 5 31 3 1 0 2 37
Total 196 54 24 7 26 307
* Others= Huawei, LG, ASUS
II. ANALYSIS OF DATA
1. THEORY AND ASSUMPTION
1.1 Estimate the percentage of the students using iPhone in each year and the
entire institute:
The results of the test are in the Binomial’s distribution which hold the pmf
p(x) = 𝑝 𝑥
(1 − p) 𝑛−𝑥
In order to conduct the estimator for the proportion, we apply the Maximum Likelihood
Estimator’s theorem(MLE) for the pmf above, then;
𝑙𝑛[𝑝(𝑥)] = 𝑥𝑙𝑛(𝑝) + (𝑛 − 𝑥)𝑙𝑛(1 − 𝑝)
⇒
𝑑
𝑑𝑝
(ln[𝑝(𝑥)]) =
𝑥
𝑝
−
𝑛 − 𝑥
1 − 𝑝
= 0
52
45
35 33 31
18
14 13
6
35 7 6 5
10
4
1 2 0
7 6 6 5
2
0
10
20
30
40
50
60
Year 1 Year 2 Year 3 Year 4 Year 5
NUMBEROFSTUDENTS
Number of students using various phone models
Iphone Samsung Nokia Sony other
4. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
4
⇔
1
𝑝
− 1 =
𝑛
𝑥
− 1
Thus, from the results in the table we can estimate the proportion of students using iPhone as
following;
The estimations of students using various phones in ITC(%)
Students iPhone Samsung Nokia Sony Others* TOTAL
Year 1 63% 22% 6% 0% 9%
100%
Year 2 59% 18% 9% 5% 8%
Year 3 57% 21% 10% 2% 10%
Year 4 65% 12% 10% 4% 10%
Year 5 84% 8% 3% 0% 5%
Entire ITC 64% 18% 8% 2% 8%
* Others= LG, Huawei, Asus
2. TEST HYPOTHESIS AND CONFIDENCE INTERVAL CONDUCTING
The estimator 𝑝 = 𝑥/𝑛 is unbiased (𝐸(𝑝) = 𝑝) has approximately a normal distribution, and
its standard deviation is 𝜎 𝑝̂ = √𝑝(1 − 𝑝)/𝑛 .
When H0 is true, 𝐸(𝑝) = 𝑝 𝑜 and 𝜎 𝑝̂ = √𝑝 𝑜(1 − 𝑝 𝑜)/𝑛 . so 𝜎 𝑝̂ does not involve any
unknown parameters.
when n is large and H0 is true, the test statistic has
𝑍 =
𝑝 − 𝑝0
√𝑝0(1 − 𝑝0)/𝑛
~𝒩(0,1)
If the alternative hypothesis is 𝐻 𝑎: 𝑝 > 𝑝 𝑎 and the upper-tailed rejection region𝑧 > 𝑧 𝛼 is
used, then
63%
59% 57%
65%
84%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
0 1 2 3 4 5 6Year
The tendancy of students using certain phone models from
year 1 to 5
iPhone Samsung Nokia Sony Others
𝑝 =
𝑥
𝑛
5. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
5
𝑃(𝑡𝑦𝑝𝑒 𝐼 𝑒𝑟𝑟𝑜𝑟 ) = 𝑃(𝑟𝑒𝑗𝑒𝑐𝑡 𝐻0 𝑤ℎ𝑒𝑛 𝐻0 𝑖𝑠 𝑡𝑟𝑢𝑒 )
= 𝑃(𝑧 > 𝑧 𝛼 𝑤ℎ𝑒𝑛 𝑧 ℎ𝑎𝑠 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑛𝑜𝑟𝑚𝑎𝑙 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛) = 𝛼
Which, 𝑍 𝛼is the critical value that is calculated by using standard normal table.
𝑃(𝑧 < 𝑧 𝛼) = 1 − 𝛼
𝜙(𝑧 𝛼) = 1 − 𝛼
Note: The assumption above is stated in the condition that 𝒏𝒑 𝒐 > 𝟏𝟎 𝒂𝒏𝒅 (𝟏 − 𝒑 𝟎) > 𝟏𝟎
Standardizing 𝑝 by subtracting p and dividing by 𝜎 𝑝̂ then implies that
𝑃
(
−𝑧 𝛼
2
<
𝑝 − 𝑝
√ 𝑝(1 − 𝑝)
𝑛
< 𝑧 𝛼/2
)
≈ 1 − 𝛼
By simplifying this equation, we get the confidence interval for population proportion p with
confidence level approximately 100(1 − 𝛼)%
𝑝̃ − 𝑧 𝛼
2
√ 𝑝̂𝑞̂
𝑛
+
𝑧 𝛼/2
2
4𝑛2
1+
𝑧 𝛼
2
2
𝑛
< 𝑝 < 𝑝̃ +
√𝑝̂ 𝑞̂/𝑛+𝑧 𝛼/2
2 /4𝑛2
1+𝑧 𝛼/2
2 /𝑛
, where 𝑝̃ =
𝑝̂+𝑧 𝛼/2
2
/2𝑛
1+𝑧 𝛼/2
2 /𝑛
III. STATISTICAL ANALYSIS
1.1 Test the proportion of the students in each year using iPhone whether the true
proportion exceed 50% at level 𝜶 = 𝟎. 𝟎𝟓
Test hypothesis 𝐻 𝑜 ∶ 𝑝0 = 0.5 𝑣𝑠 𝐻 𝑎 ∶ 𝑝 𝑎 > 0.5
Test statistic:
𝑍 =
𝑝 − 𝑝
√𝑝(1 − 𝑝)/𝑛
These test procedures are valid provided that 𝒏𝒑 𝟎 ≥ 𝟏𝟎 and 𝒏(𝟏 − 𝒑 𝟎) ≥ 𝟏𝟎
Since 𝒏𝒊 𝒑𝒊 > 𝟏𝟎 𝒂𝒏𝒅 (𝟏 − 𝒑𝒊) > 𝟏𝟎, so the assumption above is true.
Under 𝐻0 𝑧 =
𝑝̂−0.5
√𝑝0(1−0.5)/𝑛
a) For students in year 𝟏:
𝑝 =
𝑥
𝑛
=
52
82
= 0.64
Or 100(1 − 𝛼)% CI = ( 𝑝̃ ± 𝑧 𝛼/2
√ 𝑝̂ 𝑞̂/𝑛+𝑧 𝛼/2
2 /4𝑛2
1+𝑧 𝛼/2
2 /𝑛
)
6. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
6
𝑧 𝛼 = 1.645
𝛼
𝑧 = 1.61
𝑧 =
𝑝̂−𝑝0
√𝑝(1−𝑝)/𝑛
=
0.64−0.5
√0.5(1−0.5)/82
=2.536
Find 𝒛∝ at level ∝= 𝟎. 𝟎𝟓:
P (𝑧∝)=1- 𝛼 = 1 − 0.05 = 0.95
From table 𝑧 𝛼 = 1.645
Rejection region RR={𝑧|𝑧 > 𝑧 𝛼}={𝑧|𝑧 > 1.645}
Since 𝑧 = 5.36 > 𝑧 𝛼 = 1.645 , we reject 𝐻0
Conclusion: There are strong evidence to conclude that the true proportion of
students using iPhone in year 1 exceeds 50%.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
We have;
𝑝̃ ± 𝑧 𝛼/2
√𝑝̂ 𝑞̂/𝑛+𝑧 𝛼/2
2 /4𝑛2
1+𝑧 𝛼/2
2 /𝑛
, where 𝑝̃ =
𝑝̂+𝑧 𝛼/2
2
/2𝑛
1+𝑧 𝛼/2
2 /𝑛
𝑝̃ =
0.63 + 1.962
/2 × 82
1 + 1.962/82
= 0.62
𝑧 𝛼/2
√𝑝̂ 𝑞̂/𝑛+𝑧 𝛼/2
2 /4𝑛2
1+𝑧 𝛼/2
2 /𝑛
= 1.96
√0.63×0.47+1.962/4×822
1+1.962/82
=0.11
b) For students in year 2:
𝑝 =
𝑥
𝑛
=
45
76
= 0.59
𝑧 =
𝑝 − 𝑝0
√𝑝(1 − 𝑝)/𝑛
=
0.59 − 0.5
√0.5(1 − 0.5)/76
= 1.61
Rejection Region 𝑅𝑅 = {𝑧|𝑧 > 𝑧 𝛼} = {𝑧|𝑧 > 1.645}
Since 𝑧 ∉ 𝑅𝑅, so we do not reject H0
Conclusion: There is no compelling evidence to conclude that the true proportion of
students in year 2 using iPhone exceed 50% at level 𝛼 = 0.05.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
𝑝̃ =
0.59 + 1.962
/2 × 76
1 + 1.962/76
= 0.58
𝑧 𝛼 = 1.645
𝛼
𝑧 = 2.536
⇒ 95%CI(p) = (𝟎. 𝟓𝟏, 𝟎. 𝟕𝟑)
7. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
7
𝑧 𝛼 = 1.645
𝛼
𝑧 = 2.536
𝑧 𝛼 = 1.645
𝛼
𝑧 = 1.15
𝑧 𝛼/2
√ 𝑝 𝑞̂/𝑛 + 𝑧 𝛼/2
2
/4𝑛2
1 + 𝑧 𝛼/2
2
/𝑛
=
√0.59 × 0.41 + 1.962/4 × 762
1 + 1.962/76
= 0.11
c) For students in year 3:
𝑝 =
𝑥
𝑛
=
35
62
= 0.57
𝑧 =
𝑝 − 𝑝0
√𝑝(1 − 𝑝)/𝑛
=
0.57 − 0.5
√0.5(1 − 0.5)/61
= 1.15
Rejection Region 𝑅𝑅 = {𝑧|𝑧 > 𝑧 𝛼} = {𝑧|𝑧 > 1.645}
Since 𝑧 ∉ 𝑅𝑅, so we do not reject H0
Conclusion: There is no compelling evidence to conclude that the true proportion of
students in year 3 using iPhone exceed 50% at level 𝛼 = 0.05.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
𝑝̃ =
0.57 + 1.962
/2 × 61
1 + 1.962/61
= 0.56
𝑧 𝛼/2
√ 𝑝 𝑞̂/𝑛 + 𝑧 𝛼/2
2
/4𝑛2
1 + 𝑧 𝛼/2
2
/𝑛
= 1.96
√0.57 × 0.43 + 1.962/4 × 612
1 + 1.962/61
= 0.12
d) For students in year 4:
𝑝 =
𝑥
𝑛
=
33
51
= 0.65
𝑧 =
𝑝 − 𝑝0
√𝑝(1 − 𝑝)/𝑛
=
0.65 − 0.5
√0.5(1 − 0.5)/51
= 2.10
Rejection Region 𝑅𝑅 = {𝑧|𝑧 > 𝑧 𝛼} = {𝑧|𝑧 > 1.645}
Since 𝑧 ∈ 𝑅𝑅, so we reject H0
Conclusion: There is compelling evidence to conclude that the true proportion of
students in year 4 using iPhone exceed 50% at level 𝛼 = 0.05.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
⇒ 95%CI(p) = (𝟎. 𝟒𝟒, 𝟎. 𝟔𝟖)
⇒ 95%CI(p) = (0.47, 0.69)
8. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
8
𝑧 𝛼 = 1.645
𝛼
𝑧 = 4.11
𝑧 𝛼 = 1.645
𝛼
𝑧 = 4.85
𝑝̃ =
0.53 + 1.962
/2 × 82
1 + 1.962/82
= 0.64
𝑧 𝛼/2
√ 𝑝 𝑞̂/𝑛 + 𝑧 𝛼/2
2
/4𝑛2
1 + 𝑧 𝛼/2
2
/𝑛
= 1.96
√0.53 × 0.47 + 1.962/4 × 822
1 + 1.962/82
= 0.13
e) For students in year 5:
𝑝 =
𝑥
𝑛
=
31
37
= 0.84
𝑧 =
𝑝 − 𝑝0
√𝑝(1 − 𝑝)/𝑛
=
0.84 − 0.5
√0.5(1 − 0.5)/37
= 4.11
Rejection Region 𝑅𝑅 = {𝑧|𝑧 > 𝑧 𝛼} = {𝑧|𝑧 > 1.645}
Since 𝑧 ∈ 𝑅𝑅, so we reject H0
Conclusion: There is compelling evidence to conclude that the true proportion of
students in year 5 using iPhone exceed 50% at level 𝛼 = 0.05.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
𝑝̃ =
0.84 + 1.962
/2 × 37
1 + 1.962/37
= 0.81
𝑧 𝛼/2
√ 𝑝 𝑞̂/𝑛 + 𝑧 𝛼/2
2
/4𝑛2
1 + 𝑧 𝛼/2
2
/𝑛
= 1.96
√0.84 × 0.16 + 1.962/4 × 372
1 + 1.962/37
= 0.63
f) For entire students in ITC:
𝑝 =
𝑥
𝑛
=
196
307
= 0.64
𝑧 =
𝑝 − 𝑝0
√𝑝(1 − 𝑝)/𝑛
=
0.64 − 0.5
√0.5(1 − 0.5)/307
= 4.85
Rejection Region 𝑅𝑅 = {𝑧|𝑧 > 𝑧 𝛼} = {𝑧|𝑧 > 1.645}
Since 𝑧 ∈ 𝑅𝑅, so we reject H0
⇒ 95%CI(p) = (𝟎. 𝟔𝟖, 𝟎. 𝟗𝟒)
⇒ 95%CI(p) = (𝟎. 𝟓𝟏, 𝟎. 𝟕𝟕)
9. Institute of Technology of Cambodia 2016-2017 Case study: Smartphone Preference
1). Khen Chanthorn 2). Kech Sengthai 3). Ken Keomhong 4). Kam Chanreaksmee
5). Kry Reothea
9
Conclusion: There is enough evidence to conclude that the true proportion of students
in ITC using iPhone from year 1 to year 5 exceed 50% at level 𝛼 = 0.05.
Confidence Interval for proportion at level 𝜶 = 𝟎. 𝟎𝟓
𝑝̃ =
0.53 + 1.962
/2 × 82
1 + 1.962/82
= 0.64
𝑧 𝛼/2
√ 𝑝 𝑞̂/𝑛 + 𝑧 𝛼/2
2
/4𝑛2
1 + 𝑧 𝛼/2
2
/𝑛
= 1.96
√0.53 × 0.47 + 1.962/4 × 822
1 + 1.962/82
= 0.05
IV. CONCLUSION
After doing survey and conducting the estimation and test hypothesis, we found that the
most popular smartphone model is iPhone. However, the test hypothesis showed that at level
𝛼 = 0.05 _equilibrium the 95% Confidence Interval, the true proportion of students using
iPhone in year 1, year 4 and year 5 exceed 50% whereas there are no enough evidence to
conclude that the true proportion of students in year 2 and year 3 exceed 50%.
3. Our interest in this case study:
Even though this is just a small case study, but it gave us good experiences in doing team
work and the tactic in collecting data. Furthermore, this case study is also the revision of the
lessons that we have learnt.
⇒ 95%CI(p) = (0.59,0.69)