Answer Sheet of Internal exam 2018, Statistics

Business Research Methodology (MSR 532) M.Sc.Ag. (ABM), 3rd
Semester
1
Note: Solved by Basudev Sharma with the help of class note and web search.
Basu
H I C A S T , K a t h m a n d u
Internal Assessment - 2075
Candidates are requested to give their answer in their own words as far as possible.
The figures in the margin of each group indicate Full Marks. Assume suitable data if necessary.
A. Long Question: Attempt any TWO questions. 2 x 10 = 20
1. How do you relate the research proposal with research? Explain briefly the
components/ elements of a research proposal.
Answer:
According to Adhikari (2003), Research is a fact-finding process. It may
verify old facts or discover new facts on a specific topic. A research proposal
is a plan or an arrangement for doing or organizing something an
imaginative scheme. Research proposal and research can be relate as follow,
• Research proposal is a plan, and research is action.
• Research proposal is compulsory for approving proposed research.
• Research proposal is a schedule and research is activity.
• Research proposal is a mirror of research
• Research proposal is a blue print of research.
• Research proposal can serve as a document of contract for the project.
Element of Research proposal:
1. Title
2. Introduction/Background Information
3. Statement of the problem
4. Literature review /Theoretical framework
5. Objectives/ Hypotheses
6. Significance of the study
7. Research Methods and Procedures
a. Research design,
b. Subjects or Participants,
c. Instruments,
d. Work Plan/Procedure,
e. Analysis

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8. Gantt chart
9. Budget
10. Acronyms
11. Expected Results/Outcomes
12. Appendices
13. References
Brief explanation of elements of the research proposal
1. Title
 Precise and accurate
 Unambiguous
• Avoid extremely long titles
2. Introduction/Background Information
• Orient the readers towards the topic.
• The context from which the research problem emerges.
• Explain the importance and relevance of the topic
• Justifies the choice of the topic.
• Research question/hypothesis.
3. Statement of the problem
• It is the focal point of your research.
• Effective problem statement answers the question "Why does this
research need to be conducted?"
• Should indicate why the researcher needs to be done and what will be its
relevance.
• Conveys information about a research problem.
• The problem statement is just one sentence, with several paragraphs of
elaboration.

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Example: The compulsory retirement from the service at the age of 58
years old, is creating fear, anxiety, and a loss of productivity in
employees of civil services of Nepal.
4. Literature review /Theoretical framework
• It shares with the reader the results of other studies that are closely related
to the study being reported ( Fraenkel &Wallen, 1990)
• It prevents the duplication of work that has been done before.
Theoretical framework: The theorized relationship as visualized by the
researcher should be presented.
Seeing is believing: Use schematic figures or diagrams to help reviewers
understand your model and idea
5. Objectives/ Hypotheses/Definition of Terms used
Objective of study
• The general objective of a study states what researcher expects to
achieve by the study in general terms.
• Research objectives are the goals to be achieved by conducting the
research. They may be stated as ‘general’ and ‘specific’.
Hypotheses
• Build the case to support the hypothesis with literature and data.
• State your hypotheses and alternative hypothesis clearly.
Definition of Terms used
• If the study uses any term which does not have well-accepted
definition, it should be defined.
6. Significance of the study
• Indicate how your study will refine, revise, or extend existing
knowledge in the area under investigation.
• The significance of the study answers the questions:

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– Why is your study important?
– To whom is it important?
– What benefits will occur if your study is done?
7. Research Methods and Procedures:
The methods section describes the rationale for the application of specific
procedures or techniques used to identify, select, and analyze information
applied to understanding the research problem, thereby, allowing the reader to
critically evaluate a study’s overall validity and reliability. The methodology
section of a research paper answers two main questions: How was the data
collected or generated? And, how was it analyzed? The writing should be
direct and precise and always written in the past tense.
 This section is very important and known as heart of the research
proposal because it tells your evaluators how you plan to tackle your
research problem.
 It will provide your work plan and describes the activities necessary for
the completion of your project.
 The activities should be described with as much detail as possible.
 Methods should not be made explicit in the how (of their use) but also in
the why (of their selection).
The following are the major contents of this section:
a) Research design
A brief mention about the research design to be followed has to be made.
What kind of design do you plan to choose? Is it going to be a/an
• Descriptive case study
• Experimental study
• Mixed Method
• Quantitative Method Design
• Qualitative Method Design

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b) Subjects or Participants
 The population of the study
 Organizational details
 Sample size and sampling methods
c) Instruments
• Sources of data and data collecting instruments
• What kind of measuring instruments or questionnaire do you plan to use?
• Why do you choose them?
• Are they valid and reliable?
d) Work Plan/Procedure
• Include the major phases of the project:
• Estimate when you will start each stage of the work, and how long it will
take.
• Sequencing, flow and timeline of the study.
e) Analysis:
• The analysis of data (test of hypothesis) and the statistical tools to be
applied are to be mentioned
8. Gantt chart
A Gantt chart is an overview of tasks/proposed activities and a time frame
for the same. You put weeks, days or months at one side, and the tasks at the
other. You draw fat lines to indicate the period the task will be performed to
give a timeline for your research study.
9. Budget
A proposal must have budget with item wise/activity wise breakdown and
justification for the same. Budget has indicates how much financial
requirement will be essential to complete the study. It gives expenditure plan
as well with calendar of expenditure.

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10. Acronyms
An acronym is a word composed of the first letters of the words in a
phrase, especially when this is used as a name. Acronyms are essential to
define the abbreviations used in the proposal which give clear on that to the
reader.
11. Expected Results/Outcomes
• Your research proposal should be concluded by addressing your predicted
outcomes.
• What are you hoping to prove/disprove?
• Indicate how you envisage your research will contribute to debates,
discussions, or practices in your particular subject area:
 How will your research make an original contribution to
knowledge?
 How might it fill gaps in existing work?
 How might it extend understanding of particular topics?
 How might it contribute to the solution of the problem or issue
under investigation?
12. Appendices
Appropriate appendixes should be included in the proposal. For example:
Interview protocols, sample of informed consent forms, cover letters sent to
appropriate stakeholders, official letters for permission to conduct research.
Regarding original scales or questionnaires, if the instrument is copyrighted
then permission in writing to reproduce the instrument from the copyright
holder or proof of purchase of the instrument must be submitted.
13. References
• List all references cited in the proposal. Make sure these references are:–
• Up-to-date
• Relevant
• Original source
The published source of information and literature consulted in the course of
proposal preparation should be alphabetically listed.

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2. What is probability sampling? List the techniques of probability sampling.
Explain the selection process of one of the techniques with its advantage and
disadvantage.
Answer:
Probability Sampling is a sampling technique in which sample from a larger
population are chosen using a method based on the theory of probability. For
a participant to be considered as a probability sample, he/she must be
selected using a random selection.
The most important requirement of probability sampling is that everyone in
your population has a known and an equal chance of getting selected. For
example, if you have a population of 100 people every person would have
odds of 1 in 100 for getting selected. Probability sampling gives you the best
chance to create a sample that is truly representative of the population.
Probability sampling uses statistical theory to select randomly, a small group
of people (sample) from an existing large population and then predict that all
their responses together will match the overall population.
Types of Probability Sampling
 Simple Random Sampling
 Stratified Random Sampling
 Cluster Random Sampling
 Systematic Sampling
Selection process of Simple Random Sampling:
Simple random sampling as the name suggests is a completely random
method of selecting the sample. This sampling method is as easy as
assigning numbers to the individuals (sample) and then randomly choosing
from those numbers through an automated process. Finally, the numbers that
are chosen are the members that are included in the sample.

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There are two ways in which the samples are chosen in this method of
sampling: Lottery system and using number generating software/ random
number table. This sampling technique usually works around large
population and has its fair share of advantages and disadvantages.
Advantages of Simple Random Sampling:
1. Better chances that the sample represents the whole population
2. Can be concluded in shorter time duration
3. Costs less money
4. Involves lesser degree of judgment
5. Comparatively easier way of sampling
6. Can be done even by non- technical persons too
7. Easy to conduct
8. High probability of achieving a representative sample
9. Meets assumptions of many statistical procedures
Disadvantages of Simple Random Sampling:
1. Identification of all members of the population can be difficult
2. Contacting all members of the sample can be difficult
3. Risks of selecting samples from a few variations only
4. Redundant and monotony

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3. An experiment was conducted by a student in Genetics Laboratory on pea-
breeding and obtained the frequency of 4 groups namely: A, B, C, D as 810,
415, 305, and 102. Mendalian theory predicts that the frequencies of these
groups should be in the proportion of 9:3:3:1. Do the experimental results
support the theory of Mendal at 5% level of significance? (Tabulated value
of X2
at 0.05 for 4 df = 9.49, 3 df = 7.815)
Answer:
a) Setting hypothesis:
Ho: The given data are consistent with the Mendalian theory i.e. the
theory fits the data appropriately
Ha: The given data aren't consistent with the Mendalian theory i.e. the
theory doesn't fit the data appropriately
b) Level of significance (α) = 5%
c) Test statistics: Chi-square (X2
) test
d) Computation:
Group
Type
Observed
Value (O)
Expected
Ratio
Expected
Value (E)
O - E (O – E)2
A 810 9
1632 x 9/16
= 918
-108 11664 12.705
B 415 3
1632 x 3/16
= 306
109 11881 38.827
C 305 3
1632 x 3/16
= 306
-1 1 0.003
D 102 1
1632 x 1/16
= 102
0 0 0
Total 1632 16 1632 0 23546 51.535
Calculated X2
value is 51.535 and tabulated X2
value at 0.05 for 3 df is 7.851
e) Decision:
Calculated X2
value is greater than tabulated X2
value. So that null
hypothesis is rejected and alternate hypothesis is accepted. It means that the
given data aren't consistent with the Mendalian theory i.e. the theory doesn't
fit the data appropriately.

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4. The average yield of mustard obtained from 10 farms from Chitwan in 2007
was 2.635 ton/ha with standard deviation (s) 1.4 ton/ha. It is known that in
2005 the average of the yield recorded on all the farms growing mustard in
Chitwan had been 1.8 ton/ha. Test the assumption at 5% level of significance
that the average yield of mustard in Chitwan had not changed between two
years. (t a/2 9 df = 2.26)
Answer:
According to the data given above,
µ = 1.8 ton/ha
x⁻ = 2.635 ton/ha
s = 1.4 ton/ha
n = 10
t = 2.26 (at a/2 9 df)
a) Setting hypothesis:
Ho: There is no difference between the mean yield of mustard during
2007 and mean yield of mustard during 2005 in Chitwan
Ha: There is difference between the mean yield of mustard during 2007
and mean yield of mustard during 2005 in Chitwan
Symbolically,
Ho: µ = 1.8 ton/ha
Ha: µ ≠ 1.8 ton/ha
b) Level of significance: 5%
I would like to test at 5% level of significance which implies that the
chance of committing error, when null hypothesis (Ho) is true, is 5%.
c) Test statistics:
The number of observation is 10, which is small to justify for 't' statistics,
we also don't know the population variance. Assuming that population is
approximately normal, we can use the following formula for the
estimation.

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d) Calculation:
μ = x¯ ± t0.025, 9(df) s/√n
= 2.635 ± 2.26 (1.4/√10)
= 2.635 ± 1.00
= 1.635 to 3.635
e) Decision: Since the average yield of mustard during the 2005 lies between
the calculated value. We can't reject the null hypothesis (Ho). It implies
that based on the sample evident. It means there is no difference between
the mean yield of mustard of year 2005 and 2008. There is 5% likelihood
that the decision may be wrong.
Other method of calculation;
t =
2.635 – 1.8
=
0.835
1.4 0.442
√10
t = 1.89 (Calculated value)
t = 2.26 (Tabulated value)
Decision: Since calculated value is less than the tabulated value, the null
hypothesis is accepted. It means there is no difference between
the mean yield of mustard of year 2005 and 2008. There is 5%
likelihood that the decision may be wrong.

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B. Short Notes: Attempt any FIVE. 5 x 3 = 15
1. Why do we generally study samples in research work for generalization
rather than study the population. Explain in short with examples about the
systematic sampling process for the selection of samples.
Answer:
A sample is a portion, or part, of the population of interest. Samples study is
done for following reasons:
• The physical impossibility of checking all items in the population.
• The cost of studying all the items in the population.
• The sample results are usually adequate.
• Contacting the whole population would often be time-consuming.
• The destructive nature of certain tests.
Systematic sampling is a probability sampling method where the elements
are chosen from a target population by selecting a random starting point and
selecting other members after a fixed ‘sampling interval’. Sampling interval
is calculated by dividing the entire population size by the desired sample
size. For instance, if a local NGO is seeking to form a systematic sample of
500 volunteers from a population of 5000, they can select every 10th person
in the population to systematically form a sample. Once the numbering is
done, the researcher can select a number randomly, for instance, 5. The 5th
individual will be the first to be a part of the systematic sample. After that,
the 10th member will be added into the sample, so on and so forth (15th,
25th, 35, 45th, and members till 4995).
It’s extremely simple and convenient for the researchers to create, conduct,
and analyze samples. The factor of risk involved in this sampling method is
extremely minimal. As there’s no need to number each member of a sample,
systematic sampling is better for representing a population in a faster and
simpler manner.

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2. What type of questions to be avoided while preparing a questionnaire?
Answer:
Questionnaire is
• A set of predetermined questions for all respondents that serves as a
primary research instrument in survey research.
• Used to collect factual information
• Consist of a form containing a series of questions
The following types of questions need to be avoided in a survey or poll.
• Embarrassing Questions
Questions that ask respondents details about their personal and private
matters are embarrassing questions. Such types of questions are better to be
avoided as you risk losing trust of your respondents.
• Positive/ Negative Connotation Questions
Since most verbs, adjectives and nouns in the English language have either a
positive or negative connotations, questions are bound to be taken as either
positive or negative. While defining a question, strong negative or positive
overtones must be avoided.
• Hypothetical Questions
Hypothetical questions are based on speculation and fantasy. These
questions force respondents to give their ideas on a particular subject, and
generally the data collected through such questions are inconsistent and
unclear. Hypothetical questions should be avoided in questionnaires.
3. What is the value of coefficient of determination (R2
).
a) If explained variation is 16 and unexplained variation is 4.
b) Coefficient of correlation is 0.9.
Answer:
a) Given that
Explained Variation=16 Unexplained Variation= 4
Find, Coefficient of determination.

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We know that Coefficient of determination = Explained variation/Total
Variation
Hence R2
= 16/(16+4)=16/20=0.8
b) Calculate R2
if coefficient of correlation is 0.9
Given that r = 0.9
Now coefficient of determination = r2
= 0.9*0.9=0.81
= 0.81 x 100 = 81%
4. Prove that the following 2 (two) sets of data have the same (equal) variation:
Set - A Set - B
Sample mean x⁻1 = 4 Sample mean x⁻2 = 48
Sample standard deviation (s1) = 1.58 Sample standard deviation (s2) = 18.97
Answer:
Set A
Sample Mean = 4
Sample SD = 1.58
Now Coefficient of Variation=sd/mean=1.58/4 = 0.395 = 0.395x100=39.5%
Set B
Sample Mean = 48
Sample SD = 18.97
Now coefficient of variation = 18.97/48= 0.395 = 0.395 x 100 = 39.5%
Since the coefficient of variation is equal for two data sets, the data set have
same variance
5. Degree of Freedom and its importance in Statistics.
Answer:
In statistics, the degrees of freedom (DF) indicate the number of independent
values that can vary in an analysis without breaking any constraints. It is an
important idea that appears in many contexts throughout statistics including
hypothesis tests, probability distributions, and regression analysis. Learn
how this fundamental concept affects the power and precision of our
statistical analysis!

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Estimates of statistical parameters can be based upon different amounts of
information or data. The number of independent pieces of information that
go into the estimate of a parameter is called the degrees of freedom (df).
Degrees of freedom are the number of independent values that a statistical
analysis can estimate. We can also think of it as the number of values that
are free to vary as you estimate parameters. Typically, the degrees of
freedom equal our sample size minus the number of parameters we need to
calculate during an analysis. It is usually a positive whole number. In sample
estimate (s) of population standard deviation (σ) we need df, i.e. n-1.
6. A valid instrument is always reliable, but a reliable instrument may not
always be valid. Justify this statement.
Answer:
Reliability is the degree to which an assessment tool produces stable and
consistent results but validity is the ability of an instrument to measure what
it is designed to measure. Validity is the ability of an instrument to measure
what it is designed to measure. Reliability is a prerequisite of validity. A
highly reliable test is always a valid measure of some function. Thus,
reliability controls validity.
Validity could be defined as a construct we are trying to define. For
example, whether a test accurately assesses a student’s understanding of a
mathematical concepts or a test that scores student’s intelligence. On the
other hand, as previously mentioned, reliability refers to the extent in which
a quiz, test or project provides consistent results. For example, a student
might achieve consistent scores on their math homework, but the homework
is not relevant to the day's math lesson. In this example, we see that the
results are reliable, but are in fact not valid. So, in this case, we could take a
look at the second figure in the diagram. The arrows are all clustered in the
same general area, but completely missed the target.

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Difference between Validity and Reliability
Simply, the validity of the measuring instrument represents the degree to
which the scale measures what it is expected to measure. It is not same as
reliability, which refers to the degree to which measurement produces
consistent outcomes.
For the purpose of checking the accuracy and applicability, a multi-item
measurement scale needs to be evaluated, in terms of reliability, validity, and
generalizability. These are certain preferred qualities which gauge the
goodness in measuring the characteristics under consideration. Validity is all
about the genuineness of the research, whereas reliability is nothing but the
repeatability of the outcomes. This article will break down the fundamental
differences between validity and reliability.
Comparison Chart of Validity and Reliability
BASIS FOR
COMPARISON
VALIDITY RELIABILITY
Meaning Validity implies the extent to
which the research instrument
measures, what it is intended
to measure.
Reliability refers to the degree
to which scale produces
consistent results, when
repeated measurements are
made.
Instrument A valid instrument is always
reliable.
A reliable instrument need not
be a valid instrument.
Related to Accuracy Precision
Value More Comparatively less.
Assessment Difficult Easy
Key Differences between Validity and Reliability
The points presented below, explains the fundamental differences between
validity and reliability:

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 The degree to which the scale gauges, what it is designed to gauge, is
known as validity. On the other hand, reliability refers to the degree of
reproducibility of the results, if repeated measurements are done.
 When it comes to the instrument, a valid instrument is always reliable,
but the reverse is not true, i.e. a reliable instrument need not be a valid
instrument.
 While evaluating multi-item scale, validity is considered more
valuable in comparison to reliability.
 One can easily assess the reliability of the measuring instrument;
however, to assess validity is difficult.
 Validity focuses on accuracy, i.e. it checks whether the scale produces
expected results or not. Conversely, reliability concentrates on
precision, which measures the extent to which scale produces
consistent outcomes.
7. Comment on "Any testing is better than no testing".
Answer:
Any testing is better than no testing because,
• People often think that testing a survey takes a long time. They think
they don’t have the time or resources for it, and so they end up just
running the survey without any testing. This is a big mistake. Even
testing with one person is better than no testing at all. So if you don’t
have the time or resources to do everything, just do as much as you
can with what you have available.
• As a general rule, you should aim to pretest all your surveys and forms
with at least 5 people. Even with this small number of people you’ll be
surprised how many improvements you can make.

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8. List the common sources of error in research design.
Answer:
The common sources of error in research design are as follows,
Random Sampling Error
• Random error- the sample selected is not representative of the
population due to chance.
• The level of it is controlled by sample size.
• A larger sample size leads to a smaller sampling error.
Non-sampling Error
• Systematic Error
The level of it is not controlled by sample size.
The basic types of non-sampling error:
A non-response error occurs when units selected as part of the sampling
procedure do not respond in whole or in part.
A response or data error is any systematic bias that occurs during data
collection, analysis or interpretation, like:
• Respondent error (e.g., lying, forgetting, etc.).
• Interviewer bias.
• Recording errors.
• Poorly designed questionnaires.
9. Suppose in a recent Exam of Subject A, your score was 1 (one) standard
deviation (sd) above the average. How many colleagues (out of 20) scored
lower than you did? (Value between 0 and 1 standard deviation (sd) is
34.1%)
Answer:
Score = 1 SD above average
Assuming the scores obtained by the students are in normal distribution,
We can say that the score is 1 unit right of the Standard normal distribution
curve
ie, 34.1 % of the area in the right hand side of the mean curve along with 50
% of the area of left handside of standard normal distribution curve represent
the score below average+ 1SD.

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Hence the percentage of student scoring less than Average + 1SD will be 50
+ 34.1= 84.1 %
Since total no of students is 20, no of students securing less than AVG + 1sd
marks will be 84.1% of 20
= 16.82=17
Hence 17 students score less than my score.
10. Differentiate the bar graph from histogram.
Answer:
Differentiate bar graph with histogram
S.N Bar Graph Histogram
1. Bar graphs are good when our
data is in categories (such as
comedy, drama etc.).
Histograms are used to show
distributions of variables while bar
charts are used to compare
variables.
2. It is best to leave gaps between
the bars of a Bar Graph, so it
does not look like a histogram.
But, when we have continuous
data (such as person's height,
then use a Histogram.
Histograms plot quantitative data
with ranges of the data grouped
into bins or intervals while bar
charts plot categorical data.
Comparison Chart of bar graph with histogram.
Basis for
Comparison
Bar Graph Histogram
Meaning Bar graph is a pictorial
representation of data that uses
bars to compare different
categories of data.
Histogram refers to a graphical
representation that displays data
by way of bars to show the
frequency of numerical data.
Indicates Comparison of discrete
variables
Distribution of non-discrete
variables
Presents Categorical data Quantitative data
Spaces Bars do not touch each other,
hence there are spaces between
bars.
Bars touch each other, hence
there are no spaces between bars
Elements Elements are taken as
individual entities.
Elements are grouped together,
so that they are considered as
ranges.
Can bars be
reordered?
Yes No
Width of bars Same Need not to be same

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C. Short Question: Attempt any FIVE questions 5 x 1 = 5
1. What are the facts/principles of the "sampling distribution of the mean"?
Answer:
There are mainly 2 important facts (principles) could be drawn.
a) The mean of the sampling distribution of the mean is equal to the
population mean which is always true.
b) It is always true that the mean of the sampling distribution of the variance
equals the population variance.
2. Differentiate between questionnaire and schedule.
Answer:
Comparison Chart between questionnaire and schedule data collection
Basis for
Comparison
Questionnaire Schedule
Meaning
Questionnaire refers to a
technique of data collection
which consists of a series of
written questions along with
alternative answers.
Schedule is a formalized set of
questions, statements and spaces
for answers, provided to the
enumerators who ask questions
to the respondents and note
down the answers.
Filled by Respondents Enumerators
Response
Rate
Low High

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Basis for
Comparison
Questionnaire Schedule
Coverage Large Comparatively small
Cost Economical Expensive
Respondent's
identity
Not known Known
Success
relies on
Quality of the questionnaire
Honesty and competence of the
enumerator.
Usage
Only when the people are
literate and cooperative.
Used on both literate and
illiterate people.
3. Give just one clear/good example of Type II error in hypothesis testing.
Answer:
A Type II error (sometimes called a Type 2 error) is the failure to reject a
false null hypothesis. The probability of a type II error is denoted by the beta
symbol β. Good example should be,
Type I error: If you accept non pregnant woman as pregnant woman. It
does not affect so much.
Type II error: If you accept a man with pregnant man. It affects a lot,
because a man can never be pregnant.
4. What are the key points of literature review?
Answer:
Key points of a literature review
• What the research says (Theory)
• How the research was carried out (Methodology)
• What is missing or the gap that research intends to fill (Research gap)

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5. Calculate the value of population standard deviation, if the sample no. is 5,
and √∑(X - X⁻)2
is 10.
Answer:
Given that
Sample no = 5 and √∑(X-X⁻)2
= 10
Formula to calculate population standard deviation is,
s = √10/5-1 = √2.5 = 1.58
6. Why arithmetic mean is superior among others in central tendency?
Answer:
Arithmetic mean is the simplest average, easy to understand and calculate. It
is rigidly defined and is based on all the observations. It is a calculated value,
and does not depend on the position in the series. It is capable of further
algebraic treatment.
Among all the averages, AM is affected least by fluctuations of sampling.
Due to this reason AM is also called a stable average and hence superior
among others in central tendency.
7. What are the merits and demerits of Secondary data?
Answer:
Merits and demerits of secondary data are as below:
Merits
 Quick and cheap source of data
 Wider geographical area
 Leading to find primary data

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Demerits
 No fulfill our specific research needs
 Poor accuracy
 Data are not up to date
 Poor accessibility in some cases
8. What is validity? And why is it necessary?
Answer:
Validity is described as the degree to which a research study measures what
it intends to measure or it is the ability of an instrument to measure what it is
designed to measure. There are two main types of validity, internal and
external. Internal validity refers to the validity of the measurement and test
itself, whereas external validity refers to the ability to generalize the findings
to the target population. Both are very important in analyzing the
appropriateness, meaningfulness and usefulness of a research study.
Why is it necessary:
 While reliability is necessary, it alone is not sufficient.
 For a test to be reliable, it also needs to be valid.
 For example, if your scale is off by 5 lbs, it reads your weight every
day with an excess of 5 lbs.
 The scale is reliable because it consistently reports the same weight
every day, but it is not valid because it adds 5 lbs to your true weight.
 It is not a valid measure of your weight.
If the results of a study are not deemed to be valid then they are meaningless
to our study. If it does not measure what we want it to measure then the
results cannot be used to answer the research question, which is the main aim
of the study. These results cannot then be used to generalize any findings
and become a waste of time and effort. It is important to remember that just
because a study is valid in one instance it does not mean that it is valid for
measuring something else.

Semester
24
Basu
9. Differentiate between covariance and correlation.
Answer:
The following points are noteworthy so far as the difference between
covariance and correlation is concerned:
i. A measure used to indicate the extent to which two random variables
change in tandem is known as covariance. A measure used to
represent how strongly two random variables are related known as
correlation.
ii. Covariance is nothing but a measure of correlation. On the contrary,
correlation refers to the scaled form of covariance.
iii. The value of correlation takes place between -1 and +1. Conversely,
the value of covariance lies between -∞ and +∞.
iv. Covariance is affected by the change in scale, i.e. if all the value of
one variable is multiplied by a constant and all the value of another
variable are multiplied, by a similar or different constant, then the
covariance is changed. As against this, correlation is not influenced by
the change in scale.
v. Correlation is dimensionless, i.e. it is a unit-free measure of the
relationship between variables. Unlike covariance, where the value is
obtained by the product of the units of the two variables.
10. Differentiate between standard deviation and standard error of the mean.
Answer:
• Standard deviation is the average difference between the mean and
individual items of a particular sample.
• Standard error is the difference between sample mean from population
mean

Semester
25
Basu
Comparison Chart of standard deviation and standard error of the mean
Basis for
Comparison
Standard Deviation Standard Error
Meaning Standard Deviation implies a
measure of dispersion of the set
of values from their mean.
Standard Error connotes the
measure of statistical exactness
of an estimate.
Statistic Descriptive Inferential
Measures How much observations vary
from each other.
How precise the sample mean to
the true population mean.
Distribution Distribution of observation
concerning normal curve.
Distribution of an estimate
concerning normal curve.
Formula Square root of variance Standard deviation divided by
square root of sample size.
Increase in
sample size
Gives a more specific measure
of standard deviation.
Decreases standard error.
11. Why coefficient of variation (CV) is important in comparison of standard
deviation (σ)?
Answer:
The coefficient of variation is useful because the standard deviation of data
must always be understood in the context of the mean of the data. In
contrast, the actual value of the CV is independent of the unit in which the
measurement has been taken, so it is a dimensionless number. For
comparison between data sets with different units or widely different means,
one should use the coefficient of variation instead of the standard deviation.
12. List the various methods used for data collection.
Answer:
There are a variety of techniques or methods to use when gathering primary
data. Listed below are some of the most common data collection techniques.
♣ Observation method
♣ Interview method
 Structured interviews
 Unstructured interviews
 Semi structured interviews
 Focus group interviews
 Telephonic interviews
 In depth interviews
♣ Questionnaire method
♣ Schedule method

Answer Sheet of Internal exam 2018, Statistics

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Answer Sheet of Internal exam 2018, Statistics