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Alama Iqbal Open University Islamabad
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Assignment NO. 2
Business Mathematics and Statistical (MBA-5528)
Topic: ESTEMATION AND HYPOTHESIS TESTING
Submitted to: Sir Aftab Ahmad khanSubmitted by: Faizullah khan
Roll no. AH-522997 cell (0346-9175441)
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ACKNOWLEDGEMENT
All praises to Almighty Allah, the most Gracious, the most
Beneficent and the most Merciful, who enabled me to
complete this assignment.
I feel great pleasure in expressing my since gratitude to my
teacher, for his guidance and support for providing me an
opportunity to complete a productive research study of my
topic
Estimation and hypothesis testing
My special thanks and acknowledgments to Mr.Sarfaraz for
providing me all relative information, guidance and support
to compile the practical study of Engro food (pvt)
I will keep my hopes alive for the success of given task to
submit this report to my honorable teacher Sir AftabAhmad Khan whose guidance; support and encouragement
enable me to complete this assignment.
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EXECUTIVE SUMMARY
This assignment is a research-oriented activity,
which represents both the theoretical and practical
implication of the topic. In the first section of this
assignment, I explain the theoretical aspect of the
topic and all major parts has been explained which
are involved in the method of for Estimation and
Hypothesis testing For empirical study, I select
Engro food company.
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Table of Contents Page No
Title page 01
Acknowledgement 03
Abstract 04
Table of contents 05
Introduction to the issue 06
Case study 9
Data collection methods 17
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2) Presentation of data
3) Analysis of data
4) Interpretation of data
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After the collection of data and performing the statistic
procedure upon the raw data, it has become secondary data
which has become information and is useful for the user.
The user of this data uses it to estimate about the parameter
of the concern population, this procedure and stage of
statistic collection is called estimation.
n statistics, estimation refers to the process by which one
makes inferences about a population, based on information
obtained from a sample.
Point Estimate vs. Interval Estimate:
Statisticians use sample statistics to estimate populationparameters.
For example, sample means are used to estimate population means; sample
proportions, to estimate population proportions.
An estimate of a population parameter may be expressed in two ways:
Point estimate. A point estimate of a population parameter is a single
value of a statistic. For example, the sample mean x is a point estimate
of the population mean . Similarly, the sample proportionp is a point
estimate of the population proportion P.
Interval estimate. An interval estimate is defined by two numbers,
between which a population parameter is said to lie. For example, a
110 lbs (iii) H : < 110 lbs.
Setting up levels of significance:
Once the null hypothesis is set up, the next job is to set the limits within
which we expect (the null hypothesis) m lies. The idea behind it is to ensure
that the difference between the sample value and the hypothesis should arise
due to sampling fluctuations alone. If this difference does not exceeds this
limit then the sample supports the null hypothesis and the sample is
accepted. If it exceeds this limit the sample does not support the hypothesis
and it is rejected.
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Now fixing the limits totally depends upon the accuracy desired. Generally
the limits are fixed such that the probability that the difference will exceeds
the limits is 0.05 or 0.01. These levels are known as the 'levels of
significance' and are expressed as 5% or 1% levels of significance. Rejection
of null hypothesis does not mean that the hypothesis is disproved.
It simply means that the sample values does not support the hypothesis.
Also, acceptance does not mean that the hypothesis is proved. It means
simply it is being supported.
Confidence limits
The limits (or range) within which the hypothesis should lie with specified
probabilities are called the confidence limits or fiducial limits. It is
customary to take these limits as 5% or 1% levels of significance. If sample
values lies between the confidence limits, the hypothesis is accepted; if it
does not, the hypothesis is rejected at the specified level of significance.
Errors in Testing Of Hypothesis
In testing any hypothesis, we get only two results: either we
accept or we reject it. We do not know whether it is true or
false. Hence four possibilities may arise.
The hypothesis is true but test rejects it (Type I error)
The hypothesis is false but test accepts it (Type II error)
The hypothesis is true and test accepts it (correct decision)
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The hypothesis is false and test rejects it (correct decision)
In a statistical hypothesis testing experiment there are two
types of errors which could occur which are detailed below:-.
Type I error:
Is committed when the null hypothesis is rejected though it is true. In
terms of probability, Type I error is denoted by (alpha) where
= probability of type I error
= probability (rejecting H / H is true).
A Type II error:
is committed by not rejecting ( i.e. accepting) the null
hypothesis, when it is false. The probability of Type II error is
denoted by (beta) where
= probability of Type - II error
= probability (accepting Ho / H is false)
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Now supposes Murray, a manufacturer produces some
type of articles of good quality. A purchaser by chance
selects a sample randomly. It so happens that the sample
contains many defective articles and it leads the purchaser
to reject the whole product. Now, Murray suffers a loss even
though he has produced a good article of quality. Therefore,
this Type I error is called "producers risk".
On the other hand, if we accept the entire lot on the basis of
a sample and the lot is not really good, the consumers are
put in loss. Therefore, this Type II error is called the
"consumers risk".
In practical situations, still other aspects are considered
while accepting or rejecting a lot. The risks involved for both
producer and consumer are compared. Then Type I and Type
II errors are fixed; and a decision is reached.
Type of testing
Two tail teste
The two-tailed test is a statistical test used in
inference, in which a given statistical hypothesis, H0
(the null hypothesis), will be rejected when the value
of the test statistic is either sufficiently small or
sufficiently large. This contrasts with a one-tailed
http://www.answers.com/topic/statisticshttp://www.answers.com/topic/statistical-inferencehttp://www.answers.com/topic/statistical-hypothesis-testinghttp://www.answers.com/topic/null-hypothesishttp://www.answers.com/topic/test-statistic-1http://www.answers.com/topic/statisticshttp://www.answers.com/topic/statistical-inferencehttp://www.answers.com/topic/statistical-hypothesis-testinghttp://www.answers.com/topic/null-hypothesishttp://www.answers.com/topic/test-statistic-1 -
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test, in which only one of the rejection regions
"sufficiently small" or "sufficiently large" is reselected
according to the alternative hypothesis being
selected, and the hypothesis is rejected only if the
test statistic satisfies that criterion. Alternative
names are one-sided and two-sided tests.
Suppose = 1 0
true hypothesis
H0: = 1 0
1 : is not equal to 10
There are tow type of tow tail test.
http://www.answers.com/topic/alternate-hypothesishttp://www.answers.com/topic/alternate-hypothesis -
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Right tail test
H0:. 10
H1:. 10
The reason of Z-test and T- test
Z-test T-test is known
Sample size >30
is un- know then
n
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EngroFood s History
Engro Foods (Pvt.) Limited (EFL) has beenestablished in 2005 as part of a diversification
process at the Engro Group. The plant located atSukkur on 23 acre land, has the raw milk receptioncapability of 300,000 liters per day and UHT milkcapacity of 200,000liters per day. The plant has beenestablished at a cost of Rs. 1 billion which providesdirect employment to 750 people. Engro Foods hasentered the Food business through milk processingand sale with the companys vision to pursue growth
opportunities based on country fundamentals andown strength. It also positions the company toleverage its corporate social responsibility initiativesand work closely with rural communities to promoteintegrated farming and livestock development. Thiseffort is expected to play a pivotal role in povertyalleviation and improving livelihoods of the poor inthe milk collection areas.
Vision
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"Our vision is to become a fast expanding megafoods company. To achieve our vision, the companywill initially focus on dairy by investing a substantialamount in plant, milk collection capability and
marketing. We are making concrete efforts to expandin and beyond Pakistan; through strategicinternational alliances, to eventually become global."
Engro Food
Brands:
Olpers milk
Olpers cream
Olwell
Skim milk
Tarang
Tea milk
Olpers
Olpers A well known brand of Engro Foods (Pvt.) Ltd.
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Commercially launched in March 2006
Research QuestionsQ1. What is the extent to which Olpers advertisement?
campaign has created a positioning for the product that was
desired by management?
Q2. Which one is the most effective TV channel to reach the
consumer and what is the effectiveness of the channels being
currently used?
Research Objective
To identify the acceptability and perception of Packaged milk
brands
To identify the brand Appeal of consumers towards Olpers
To discover the preferences of time and channels of TV
viewers
To identify the impact of Olpers Advertisement on
Consumer Perception
Research Design
Questionnaire
Questions correspond to the objectives
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Likert scale was utilized to give quantitative results for
positioning statements
Perception of Packaged Milk Brands
Reliability of questions was assured
Observational Study
TV Channels watched GEO news, GEO entertainment, ARY
Digital and PTV Network
Time watched: 4 pm to 12 pm during Weekend
Sampling criteria
Sample size: 200
Limited due to time constraints
Assigned by Course Instructor
Sample Unit: Individual
Household
Sampling Design
Stratified Sampling
Demographics of Sample
Housewives 22
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35 years old
SEC A1, A2 and B
Perception of Packaged Milk
Market share
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Market Share of all Brand
Quality
Quality PerceptionQuality perception of the brand
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Perception of the Packaging
TV viewing habits
TV viewing habits of the Target Audience:
Hours spent daily on watching TV
30 minutes on average
Timeslots patterns for watching TV Duration
Duration %
0-10 minutes 10
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11-30 minutes 34
31-60 minutes 42
1-3 hours 12
More then 3 hours 2
Programs and AD
TV Programs watched by Target Market
Specific programs in tandem with Advertisement to intensify
recall level
Marina Morning, Nadia Khan Show, Cooking with Raha
Indian Soaps
Advertisements remembered : Telenor, ZONG, Tapal,
Olpers, Ufone, Cooking Oil etc
Central idea
Central Idea of Ad
Moments of Happiness and enjoyment are incomplete
without Olpers
Olpers is a brand for Optimistic people
Hypothesis 01
Ho: Olpers has been ineffective in establishing its desired
positioning o 2
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Ha: Olpers has been effective in establishing its desired
positioning a> 2
Conclusion
Null hypothesis is rejected
At 10% significance level, the sample provides sufficient
evidence to conclude that since the mean is greater than 2,
therefore, Olpers has been successful in establishing its
overall positioning.
Hypothesis 02
Ho: Olpers media planning has been ineffective
Po50%
Ha: Olpers media planning has been effective
Pa>50%Conclusion
Null hypothesis is rejected
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At 5% level of significance; his sample data provides sufficient
evidence to conclude that more than 50% of the respondents have
watched the Ad, therefore, Olpers media planning has been
effective.
Finding
Most of the participants watched entertainmentand recipe channels/shows
Most of the respondents were program specificwatchers e.g. Nadia Khan Show, Cooking withRahat.
The Favorite channels among the participantswere: Geo entertainment, Hum TV, ARY, Aaj TV& Geo news
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Average Viewing Time 30minutes
Viewing Time: Most viewed time slots were
09:00 -12:00 and19:00 -22:00.
Overall positioning has been established to anextent.
The Packaging of Olpers is aligned with thebrand positioning and respondents showedfavorable attitude towards it.
SWOT Analysis
Strengths
1. Engros backOlpers is a brand of ENGRO foods.ENGRO foods can easily afford research and
development.ENGRO can distribute the brand through betterchannel
2. PR with farmers
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ENGRO has a strong bond and long term relationshipwith the farmers who are willing to supply milk to thecompany.
Weaknesses
1. Olwell TVCOlwell ad which is based on Western life style.Failed to analyze in Pakistan, where practicingMuslims reside,Ignoring the ethics, religious beliefs and cultural
values.
2. Owning Red Color.There is no color association attached to Olpers.
Opportunities
1. Increased funding by Government
Government has decided to increase farmersfunding.
2. Increased consumption of PLMEach competitor in the milk industry wants toincrease penetration of processed liquid milk.
Threats
1 Perception and Price DifferentialsConsumers perceptions and price differentials cancause a threat for the company. It is important thatOlpers comes up to the expectations of thecustomers
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For example, lose milk is still cheaper than packagedmilk and that is also one factor that people still preferto buy lose milk.
2 CompetitionsFor Olpers it might be difficult to penetrate in a
market where the loyalties exist for such brands asNestle and Haleeb.
Recommendation
Advertisements should be aired during thesetime slots 9am 12am and evening 7pm -10pm
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Proposed Channel weightage for: PTV, GeoEntertainment, ARY Digital, HUMTV
Cable movie channels as an alternate Costeffective platform for mass communication
Advertisement should be program based ratherthan channel based.
After TV, the widest reach and recall is ofBillboard advertisements
Advertisement Campaign:1. The packaged milk users appear confusedabout the true meaning of Olpers mediacommunication
2. Media content must be modified in simplerterms to reduce difference of brand imageand identity
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Reference
From the book
From google.com
From wikipedia