mb0034 assignment

8/8/2019 Mb0034 Assignment

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MBA III SEM

MB0034 RESEARCH METHODOLOGY

ASSIGNMENTS

Set 2

SUBJECT NAME: RESEARCH METHODOLOGY

SUBJECT CODE: MB0034

MD. MOSHIUR RAHMAN

Registration No: - 530910729

CENTER CODE: C02543

Page 1 of 27 Name: Md. Moshiur Rahman | Registration No: 530910729


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Q.No.1 - Write a short note on the following:

(a) Null Hypothesis

(b) What is exploratory research?

(c) What is Random Sampling?

(d) Rank Order Correlation

Ans: (a) Null Hypothesis:

A null hypothesis is a hypothesis (within the frequents context of statistical hypothesis

testing) that might be falsified using a test of observed data. Such a test works byformulating a null hypothesis, collecting data, and calculating a measure of how probable

that data was assuming the null hypothesis were true. If the data appears very

improbable (usually defined as a type of data that should be observed less than 5% of

the time) then the experimenter concludes that the null hypothesis is false. If the data

looks reasonable under the null hypothesis, then no conclusion is made. In this case, the

null hypothesis could be true, or it could still be false; the data gives insufficient evidence

to make any conclusion. The null hypothesis typically proposes a general or default

position, such as that there is no relationship between two quantities, or that there is nodifference between a treatment and the control. The term was originally coined by

English geneticist and statistician Ronald Fisher.

In some versions of statistical hypothesis testing (such as developed by Jerzy Neyman

and Egon Pearson), the null hypothesis is tested against an alternative hypothesis. This

alternative may or may not be the logical negation of the null hypothesis. The use of

alternative hypotheses was not part of Ronald Fisher's formulation of statistical

hypothesis testing, though alternative hypotheses are standardly used today.

For instance, one might want to test the claim that a certain drug reduces the chance of

having a heart attack. One would choose the null hypothesis "this drug does not reduce

the chances of having a heart attack" (or perhaps "this drug has no effect on the chances

of having a heart attack"). One should then collect data by observing people both taking

the drug and not taking the drug in some sort of controlled experiment. If the data is very

unlikely under the null hypothesis one would reject the null hypothesis, and conclude that

its negation is true. That is, one would conclude that the drug does reduce the chancesof having a heart attack. Here "unlikely data" would mean data where the percentage of



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people taking the drug who had heart attack was much less then the percentage of

people not taking the drug who had heart attacks. Of course one should use a known

statistical test to decide how unlikely the data was and hence whether or not to reject the

null hypothesis.

Symbolically presented as:

Null hypothesis = Ho

Suppose we want to test the hypothesis that the population mean is equal to the

hypothesis mean ( Ho) = 100. Then we would say that the null hypotheses are

that the population mean is equal to the hypothesized mean 100 and symbolical

we can express as Ho : = Ho = 100.

(b) Exploratory Research:

Exploratory Research is also known as formulative research. It is preliminary

study of an unfamiliar problem about which the researcher has little or no

knowledge. It is ill-structured and much less focused on pre-determined

objectives. It usually takes the form of a pilot study. The purpose of this research

may be to generate new ideas, or to increase the researchers familiarity with the

problem or to make a precise formulation of the problem or to gather information

for clarifying concepts or to determine whether it is feasible to attempt the study.

Katz conceptualizes two levels of exploratory studies. At the first level is the

discovery of the significant variable in the situations; at the second, the discovery

of relationships between variables.

Exploratory research provides insights into and comprehension of an issue or situation.

It should draw definitive conclusions only with extreme caution. Exploratory research is

a type of research conducted because a problem has not been clearly defined.

Exploratory research helps determine the best research design, data collection method

and selection of subjects. Given its fundamental nature, exploratory research often

concludes that a perceived problem does not actually exist.



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Exploratory research often relies on secondary research such as reviewing available

literature and/or data, or qualitative approaches such as informal discussions with

consumers, employees, management or competitors, and more formal approaches

through in-depth interviews, focus groups, projective methods, case studies or pilot

studies. The Internet allows for research methods that are more interactive in nature:

E.g., RSS feeds efficiently supply researchers with up-to-date information; major search

engine search results may be sent by email to researchers by services such as Google

Alerts; comprehensive search results are tracked over lengthy periods of time by

services such as Google Trends; and Web sites may be created to attract worldwide

feedback on any subject.

The results of exploratory research are not usually useful for decision-making by

themselves, but they can provide significant insight into a given situation. Although the

results of qualitative research can give some indication as to the "why", "how" and

"when" something occurs, it cannot tell us "how often" or "how many." Exploratory

research is not typically generalizable to the population at large..

(c) Random Sampling:

Probability sampling is based on the theory of probability. It is also known as

random sampling. It provides a known nonzero chance of selection for each

population element. It is used when generalization is the objective of study, and a

greater degree of accuracy of estimation of population parameters is required.

The cost and time require is high hence the benefit derived from it should justify

the costs.

The following are the types of random sampling:i) Simple Random Sampling

This sampling technique gives each element an equal and

independent chance of being selected. An equal chance means equal

probability of selection. An independent chance means that the draw

of one element will not affect the chances of other elements being

selected. The procedure of drawing a simple random sample consists

of enumeration of all elements in the population.



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i. Preparation of a List of all elements, giving them numbers in

serial order 1, 2, B, and so on, and

ii. Drawing sample numbers by using (a) lottery method, (b) a

table of random numbers or (c) a computer.

ii) Stratified Random Sampling:

This is an improved type of random or probability sampling. In this

method, the population is sub-divided into homogenous groups or

strata, and from each stratum, random sample is drawn. E.g.,

university students may be divided on the basis of discipline, and each

discipline group may again be divided into juniors and seniors.

Stratification is necessary for increasing a sample's statistical

efficiency, providing adequate data for analyzing the various sub-

populations and applying different methods to different strata. The

stratified random sampling is appropriate for a large heterogeneous

population. Stratification process involves three major decisions. Theyare stratification base or bases, number of strata and strata sample

sizes.

Stratified random sampling may be classified into:

a) Proportionate stratified sampling

b) Disproportionate stratified sampling

iii) Systematic Random Sampling

This method of sampling is an alternative to random selection. It

consists of taking Kth item in the population after a random start with

an item form 1 to kth. It is also known as fixed interval method. E.g.,

1st, 11th, and 21st --------- Strictly speaking this method of sampling is

not a probability sampling. It possesses characteristics of randomnessand some non-probability traits.



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(d) Rank Order Correlation

The version of correlation examined in the main body of Chapter 3 applies tothose cases where the values of X and of Y are both measured on an equal-

interval scale. It is also possible to apply the apparatus of linear correlation to

cases where X and Y are measured on a merely ordinal scale. When applied to

ordinal data, the measure of correlation is spoken of as the Spearman rank-

order correlation coefficient, typically symbolized as rs.

Suppose, for example, that two experts, X and Y, were asked to rank N=8 items

with respect to some dimension germane to their field of expertise

(rank#1=highest, rank#8=lowest). To make it specific, you can imagine two

physicians ranking 8 patients with respect to the severity of their disease; two

psychotherapists ranking 8 patients with respect to the likelihood of improvement;

two wine experts ranking 8 wines from best to worst; two statisticians ranking 8

statistical concepts with respect to their fundamental importance; or whatever

else it might be that strikes your fancy.

As a token of my liberal-mindednessfor I am one of those benighted souls who

find all wines to taste suspiciously like vinegarI will use the image of the wine

experts. The following table shows the rankings from 1 to 8, best to worst, of two

experts, X and Y.


wine X Y

abcdefgh

12345678

21534786


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As you can see from the accompanying graph, there is a substantial degree of

agreement between the rankings of the two experts. Plug the bivariate values of

X and Y into the formulaic structure given in the main body of Chapter 3,

r =SCXY

Sqrt [SSX x SSY]

and you will find r = +.83 r2 = .69.

As it happens, these are exactly the same values you will get when you calculate

the Spearman coefficient, rs. The simple reason for this is that r and rs are

algebraically equivalent in the case where the values of X and Y consist of two

sets of N rankings. The only advantage of rs is that the calculations are easier if

you are doing them by hand. [Note, however, that rs is precisely equal to ronly

when the rankings within X and Y are the consecutive integer values: 1, 2, 3, and

so on, with no ties. With tied ranks there will tend to be discrepancies between rs

and r. If the proportion of tied ranks is fairly large, you would be better advised to

plug your rankings for X and Y into the standard formula forr.]

The Simple Formula for rs, for Rankings without Ties

Here is the same table you saw above, except now we

also take the difference between each pair of ranks(D=XY), and then the square of each difference. All

that is required for the calculation of the Spearman

coefficient are the values of N and-D2, according to the

formula

rs = 1 6D2

N(N21)


wine X Y D D2

abcdefgh

12345678

21534786

11

211

11

2

11411114

N = 8-D2 = 14


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If this formula seems a bit odd to you, you are in good company. Generations of

statistics students have been presented with it, and generations have puzzled

over such mind- bending questions as: why do you start out with "1" and subtract

something from it? where does that N (N21) in the denominator come from?;

and, above all, how does that peculiar "6" get into the numerator?

Here are the answers to these age-old questions in a nutshell.

For any set of N paired bivariate ranks, the minimum possible value of-D2

occurs in the case of perfect positive correlation. In this case, rank 1 for X

is paired with rank 1 for Y, rank 2 for X with rank 2 for Y, and so on. Each

value ofD will accordingly be equal to zero, and so too will be the sum of

the squared values ofD.

Conversely, the maximum possible value of-D2 occurs in the case of

perfect negative correlation. This maximum possible value is in every

instance equal to

maximum-D2 =N(N21)

3

Thus, for N=8 with perfect negative correlation:T

item X Y D D2

-D2 = 168

8(821)/3 = 168

abcdefgh

12345678

87654321

7531

1357

492591192549



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The ratio of the observed-D2 to its maximum possible value will therefore

be equal to zero in the case of perfect positive correlation, to +1.0 in the case

of perfect negative correlation, and to +.50 in the case of zero correlation.

-D2

N(N21)/3=

3D2

N(N21)

Double this ratio, subtract it from 1, and voila! you have a quantity that will

be equal to +1.0 in the case of perfect positive correlation, to 1.0 in the case

of perfect negative correlation, and to zero in the case of zero correlation.

rs = 1 6D2

N(N21)

And here, finally, is the calculation ofrs for the example with which webegan:

rs = 1 6D2

N(N21)

= 1 6 x 14

8(821)

= +.83

r2s = .69

The meanings ofrs and r2s in a rank- order correlation are essentially the same as

those ofrand r2 in a correlation based on equal- interval data. For the present


wine X Y D D2

abcdefgh

12345678

21534786

11

211

11

2

11411114

N = 8-D2 = 14


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example, r2s=.69 means that the covariance between the X and Y rankings is

69% as strong as it possibly could be, and the positive sign of rs=+.83 signals

that this covariation occurs along the upward slant, with higher values of X

tending to be associated with higher values of Y, and vice versa. However,

I would not recommend taking the parallels much farther than this. In particular,

I think it would not make much sense to subject bivariate rankings to the

predictive apparatus of linear regression.

Q.No.2 Elaborate the format of a research report touching briefly on themechanics of writing.

Ans: Research report is a means for communicating research experience to

others. A research report is formal statement of the research process and it

results. It narrates the problem studied, methods used for studying it and the

findings and conclusions of the study.

The format of a research report is given below:

1. Prefatory Item

Title page

Declaration

Certificates

Preface/ acknowledgment

Table of contents List of tables

List of graphs/ figures/ charts

Abstracts or synopsis

2. Body of the Report

Introduction

Theoretical background of the topic



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Statement of the problem

Review of literature

The Scope of the study

The objectives of the study

Hypothesis to be tested

Definition of the concepts

Models if any

Design of the study

Methodology Method of data collection

Sources of data

Sampling Plan

Data collection instruments

Field work

Data processing and analysis plan

Overview of the report

Limitation of the study

Result: Findings and discussions

Summary, conclusions and recommendations

3. Reference Material

Bibliography

Appendix

Copies of data collection instruments

Technical details on sampling plan

Complex tables

Glossary of new terms used.

Mechanics of Writing:



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1. Communicate to a Specific Audience :

The first step is to known the audience, its background, and its objectives. Most

effective presentations seem live conversations or memos to a particular person

as opposed to an amorphous group. Audience identification affects presentation

decisions such as selecting the material to be included and the level of

presentation. Excessive detail or material presented at too low a level can be

boring. The audience can become irritated when material perceived as relevant is

excluded or the material is presented at too high level. In an oral presentation,

the presenter can ask audience whether they already know some of the material.

Frequently, a presentation must be addressed to two or more different audiences.

There are ways to deal with such a problem. In a written presentation, an

executive summary at the outset can provide can overview of the conclusions for

the benefit of those in the audience who are not interested in details. The

presentation must respect the audiences time constraints. A appendix can be

used to reach some people selectively, without distracting the others. Sometimes

introduction to a chapter or a section can convey the nature of the contents,which certain audiences may bypass. In an oral presentation, the presence of

multiple audiences should be recognized.

2. Structure the Presentation:

Each piece of presentation should fit into the whole, just as individual pieces fit

into a jigsaw puzzle. The audience should not be muttering. The solution to this is

to provide a well- defined structure. The structure should include an introduction,a body, and a summary. Further is to tell the audience what you are going to say,

say it and then tell them what you said. Sometimes you want to withhold the

conclusion to create interest.

Introduction should play several roles. First, It should provide audience

interest. A second function is to identify the presentations central idea or

objective. Third, it should provide a road map to the rest of the presentation sothat the audience can picture its organization and flow.



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It is better to divide the body of the presentation into two to five parts . The

audience will be able to absorb only so much information. If that information can

be aggregated into chunks, it will be easier to assimilate. Sometimes the points to

be made canot be combine easily or naturally. In the case, it is necessary to use

a longer list. One way to structure the presentation is by the research questions.

Another method that is often useful when presenting the research proposal is to

base it on the research process. The most useful presentations will include a

statement of implications and recommendations relevant to the research

purpose. However, when research lacks information about the total situation

because the research study addresses only a limited aspect of it, the ability to

generate recommendations may be limited.

The purpose of the presentation summary is to identify and underline the

important points of the presentations and to provide some repetition of their

content. The summary should support the presentation communication

objectives by helping the audience to retain the key parts o the content. Theaudience should fell that there is a natural flow from one section to another.

3. Create Audience interest:

The audience should be motivated to read or listen to the presentations major

parts and to the individual elements of each section the audience should know

why the presentation is relevant to them and why each section was included. A

section that cannot hold interest should be excluded or relegated to appendix.

The research purpose and objective are good vehicles to provide motivation. The

research purpose should specify decisions to be made and should relate to the

research questions. A presentation that focuses on those research questions and

their associated hypothesis will naturally be tied to relevant decisions and hold

audience interest. In contrast, a presentation that attempts to report on all the

questions that were included in the survey and in the cross tabulations often willbe long, uninteresting and of little value.



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As the analysis proceeds and presentation is being prepared, the researcher

should be on the lookout for results that are exceptionally persuasive, relevant,

interesting, and unusual. Sometimes, the deviant respondent with strange

answers can provide the most insight in his or her responses that are pursued

and not discarded.

4. Be Specific and Visual:

Avoid taking or writing in the abstract. If different members of the audience have

different or vague understandings of important concepts, there is a potential

problem. Terms that are ambiguous or not well known should be defined and

illustrated or else omitted. The most interesting presentations usually use specific

stories anecdotes, studies or incidents to make points.

5. Address Validity and Reliability Issues:

The presentation should help the audience avoid misinterpreting the results. The

wording of the questions, the order in which they are asked, and the samplingdesign are among the design dimensions that can lead to biased results and

misinterpretations. The presentation should not include an exhaustive description

of all the design considerations. Nobody is interested in textbook discussion of

the advantages of telephone over mail surveys or how you locate homes in an

area sampling design.

The presentation should include some indication of the reliability of the results. Atthe minimum, it always should be clear what sample size was involved. The key

results should be supported by more precise information in the form of interval

estimates or a hypothesis test. They hypothesis test basically indicates, given the

sample size, what probability exists that the results were merely an accident of

sampling. If the probability of the latter is not low, then the results probably would

not be repeated. Do not imply more precision than is warranted.

Q.No.3 Discuss the importance of case study method



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Ans: Case study is a method of exploring and analyzing the life of a social unit or

entity, be it a person, a family, an institution or a community. Case study would

depend upon wit, commonsense and imagination of the person doing the case

study. The investigator makes up his procedure as he goes along. Efforts should

be made to ascertain the reliability of life history data through examining the

internal consistency of the material.. A judicious combination of techniques of

data collection is a prerequisite for securing data that are culturally meaningful

and scientifically significant. Case study of particular value when a complex set of

variables may be at work in generating observed results and intensive study is

needed to unravel the complexities. The case documents hardly fulfill the criteria

of reliability, adequacy and representativeness, but to exclude them form any

scientific study of human life will be blunder in as much as these documents are

necessary and significant both for theory building and practice. In-depth analysis

of selected cases is of particular value to business research when a complex set

of variables may be at work in generating observed results and intensive study is

needed to unravel the complexities.

Let us discuss the criteria for evaluating the adequacy of the case history

or life history which is of central importance for case study.

John Dollard has proposed seven criteria for evaluating such adequacy as

follows:

I. The subject must be viewed as a specimen in a cultural series. That is, the

case drawn out from its total context for the purposes of study must be

considered a member of the particular culture group or community. The

scrutiny of the life histories of persons must be done with a view to identify

thee community values, standards and their shared way of life.

II. The organic motto of action must be socially relevant. That is, the action ofthe individual cases must be viewed as series of reactions to social stimuli



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o situation. In other words, the social meaning of behaviour must be taken

into consideration.

III. The strategic role of the family group in transmitting the culture must be

recognized. That is, in case of an individual being the member of a family,

the role of family in shaping his behaviour must never be overlooked.

IV. The specific method of elaboration of organic material onto social

behaviour must be clearly shown. That is case histories that portray in

detail how basically a biological organism, the man, gradually blossoms

forth into a social person, are especially fruitful.

V. The continuous related character of experience for childhood through

adulthood must be stressed. In other words, the life history must be a

configuration depicting the inter-relationships between thee persons

various experiences.

VI. Social situation must be carefully and continuously specified as a factor.

One of the important criteria for the life history is that a persons life must

be shown as unfolding it self in the context of and partly owing to specific

social situations.

VII. The life history material itself must be organized according to some

conceptual framework; this in turn would facilitate generalizations at ahigher level.

Q.No.4 - Give the importance of frequency tables and discuss the principles

of table construction, frequency distribution and class intervals

determination.

Ans: The importance of frequency tables:



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Frequency tables provide a shorthand summary of data. The importance of

presenting statistical data in tabular form needs no emphasis. Tables facilitate

comprehending masses of data at a glance; they conserve space are reduce

explanations and descriptions to a minimum. They give a visual picture of

relationships between variable and categories. They facilitate summation of item

and the detection of errors and omissions and provide a basis for computations.

It is important to make a distinction between the general purpose tables and

specific tables. The general purpose tables are primary or reference tables

designed to include large amount of source data in convenient and accessible

form. The specific purpose tables are analytical or derived ones that demonstrate

significant relationships in the data or the results of statistical analysis. Tables in

reports of government on population, vital statistics, agriculture, industries etc.,

are of general purpose type. They represent extensive repositories and statistical

information. Special purpose tables are found in monographs, research reports

and articles and reused as instruments of analysis. In research, we are primarilyconcerned with special purpose.

The principles of table construction:

There are certain generally accepted principles of rules relating to construction of

tables. They are:

1. Every table should have a title. The tile should represent a succinct

description of the contents of the table. It should be clear and concise. It

should be placed above the body of the table.

2. A number facilitating easy reference should identify every table. The

number can be centred above the title. The table numbers should run in

consecutive serial order. Alternatively tables in chapter 1 be numbered as

1.1, 1.2, 1.., in chapter 2 as 2.1, 2.2, 2.3. and so on.3. The captions (or column headings) should be clear and brief.



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4. The units of measurement under each heading must always be indicated.

5. Any explanatory footnotes concerning the table itself are placed directly

beneath the table and in order to obviate any possible confusion with the

textual footnotes such reference symbols as the asterisk (*) DAGGER (+)

and the like may be used.

6. If the data in a series of tables have been obtained from different sources,

it is ordinarily advisable to indicate the specific sources in a place just

below the table.

7. Usually lines separate columns from one another. Lines are always drawn

at the top and bottom of the table and below the captions.

8. The columns may be numbered to facilitate reference.

9. All column figures should be properly aligned. Decimal points and plus or

minus signs should be in perfect alignment.

10.Columns and rows that are to be compared with one another should be

brought closed together.

11.Totals of rows should be placed at the extreme right column and totals of

columns at the bottom.12.In order to emphasize the relative significance of certain categories,

different kinds of type, spacing and identifications can be used.

13.The arrangement of the categories in a table may be chronological,

geographical, alphabetical or according to magnitude. Numerical

categories are usually arranged in descending order of magnitude.

14.Miscellaneous and exceptions items are generally placed in the last row of

the table.15.Usually the larger number of items is listed vertically. This means that a

tables length is more than its width.

16.Abbreviations should be avoided whenever possible and ditto marks

should not be used in a table.

17.The table should be made as logical, clear, accurate and simple as

possible.



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Text references should identify tables by number, rather than by such

expressions as the table above or the following table. Tables should not

exceed the page size by photo stating. Tables those are too wide for the page

may be turned sidewise, with the top facing the left margin or binding of the

script. Where tables should be placed in research report or thesis? Some writers

place both special purpose and general purpose tables in an appendix and refer

to them in the text by numbers. This practice has the disadvantages of

inconveniencing the reader who wants to study the tabulated data as the text is

read. A more appropriate procedure is to place special purpose tables in the text

and primary tables, if needed at all, in an appendix.

Frequency Distribution and Class intervals:

Variables that are classified according to magnitude or size are often arranged in

the form of a frequency table. In constructing this table, it is necessary to

determine the number of class intervals to be used and the size of the class

intervals.

A distinction is usually made between continuous and discrete variables. A

continuous variable has an unlimited number of possible values between the

lowest and highest with no gaps or breaks. Examples of continuous variable are

age, weight, temperature etc. A discrete variable can have a series of specified

values with no possibility of values between these points. Each value of a

discrete variable is distinct and separate. Examples of discrete variable are

genders of discrete variables are gender of persons (male/female) occupation

(salaried, business, profession) car size (800cc, 1000cc, 1200cc)

In practice, all variables are treated as discrete units, the continuous variables

being stated in some discrete unit size according to the needs of a particular

situation. For example, length is described units of millimeters or a tenth of an

inch.

Class Intervals:



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Ordinarily, the number of class intervals may not be less than 5 not more than 15,

depending on the nature of the data and the number of cases being studied. After

noting the highest and lower values and the feature of the data, the number of

intervals can be easily determined.

For many types of data, it is desirable to have class intervals of uniform size. The

intervals should neither be too small nor too large. Whenever possible, the

intervals should represent common and convenient numerical divisions such as 5

or 10 rather than odd division such as 3 to 7. Class intervals must be clearly

designated in a frequency table in such a way as to obviate any possibility of

misinterpretation of confusion. For example, to present the age group of a

population, the use of intervals of 1-20, 21-50 and 50 and above would be

confusing. This may be presented as 1-20, 21-50, and above 50.

Every class interval has a mid point. For example, the midpoint of an interval 1-20

is 10.50 and the midpoint of class interval 1-25 would be 13. Once class intervals

are determined, it is routine work to count the number of cases that fall in eachinterval.

Q.No.5 - Write short notes on the following:

1 (a) Type I error and type II error.

2 (b) One tailed and two tailed test3 (c) Selecting the significance level

Ans: (a) Type I error and type II error.

In the context of testing of hypothesis there are basically two types of errors that

researchers make. We may reject Ho when Ho is true & we may accept Ho when

it is not true. The former is known as type I & the later is known as Type II. In

other words, type I error mean rejection of hypothesis which should have beenaccepted & type I error mean accepting of hypothesis which should have been



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rejected. Type I error is donated by a (alpha), also called as level of significance

of test; and type II error is donated by (beta).

Decision

Accept Ho Reject Ho

Ho (true) Correct decision Type I error (a error)

Ho (false) Type II error ( error) Correct decision

The probability of Type I error is usually determined in advance and is

understood as the level of significance of testing the hypothesis. If type I error is

fixed at 5%, it means there are about chance in 100 that we will reject Ho when

Ho is true. We can control type I error just by fixing it at a lower level. For

instance, if we fix it at 1%, we will say that the maximum probability of committing

type I error would only be 0.01.

But with a fixed sample size, n when we try to reduce type I error, the probability

of committing type II error increases. Both types of errors can not be reduced

simultaneously. There is a trade-off in business situations, decision-makers

decide the appropriate level of type I error by examining the costs of penalties

attached to both types of errors. If type I error involves time & trouble of

reworking a batch of chemicals that should have been accepted, where as type II

error means taking a chance that an entire group of users of this chemicals

compound will be poisoned, then in such a situation one should prefer a type Ierror to a type II error means taking a chance that an entire group of users of this

chemicals compound will be poisoned, then in such a situation one should prefer

a type II error. As a result one must set very high level for type I error in ones

testing techniques of a given hypothesis. Hence, in testing of hypothesis, one

must make all possible effort to strike an adequate balance between Type I &

Type II error.

(b) One Tailed and two Tailed test:



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Ans: A one- or two-tailed t-test is determined by whether the total area of a is

placed in one tail or divided equally between the two tails. The one-tailed t-test is

performed if the results are interesting only if they turn out in a particular

direction. The two-tailed t-test is performed if the results would be interesting in

either direction. The choice of a one- or two-tailed t-test effects the hypothesis

testing procedure in a number of different ways.

TWO-TAILED t-TESTS

A two-tailed t-test divides a in half, placing half in the each tail. The null

hypothesis in this case is a particular value, and there are two alternative

hypotheses, one positive and one negative. The critical value of t, tcrit, is written

with both a plus and minus sign ( ). For example, the critical value of t when

there are ten degrees of freedom (df=10) and a is set to .05, is tcrit= 2.228. The

sampling distribution model used in a two-tailed t-test is illustrated below:

ONE-TAILED t-TESTS

There are really two different one-tailed t-tests, one for each tail. In a one-tailed t-

test, all the area associated with a is placed in either one tail or the other.

Selection of the tail depends upon which direction tobs would be (+ or -) if the

results of the experiment came out as expected. The selection of the tail must be

made before the experiment is conducted and analyzed.

A one-tailed t-test in the positive direction is illustrated below:



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The value tcrit would be positive. For example when a is set to .05 with ten

degrees of freedom (df=10), tcrit would be equal to +1.812.

A one-tailed t-test in the negative direction is illustrated below:

The value tcrit would be negative. For example, when a is set to .05 with ten

degrees of freedom (df=10), tcrit would be equal to -1.812.

Comparison of One and Two-tailed t-tests

1. If tOBS = 3.37, then significance would be found in the two-tailed and thepositive one-tailed t-tests. The one-tailed t-test in the negative direction would not

be significant, because was placed in the wrong tail. This is the danger of a

one-tailed t-test.

2. If tOBS = -1.92, then significance would only be found in the negative one-tailed

t-test. If the correct direction is selected, it can be seen that one is more likely to

reject the null hypothesis. The significance test is said to have greaterpower in

this case.



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The selection of a one or two-tailed t-test must be made before the experiment is

performed. It is not "cricket" to find a that tOBS = -1.92, and then say "I really

meant to do a one-tailed t-test." Because reviewers of articles submitted for

ublication are sometimes suspicious when a one-tailed t-test is done, the

recommendation is that if there is any doubt, a two-tailed test should be done.

(c) Selecting the significance level

The hypothesis is tested on a pre-determined level of significance and such the

same should have specified. Generally, in practice, either 5% level or 1% level is

adopted for the purpose. The factors that affect the level of significance are:

The magnitude of the difference between sample ;

The size of the sample;

The variability of measurements within samples;

Whether the hypothesis is directional or non directional (A directional

hypothesis is one which predicts the direction of the difference between,say, means). In brief, the level of significance must be adequate in the

context of the purpose and nature of enquiry.

Q.No.6 - Explain Karl Pearson Co-efficient of correlation. Calculate Karl

Pearson coefficient for the following data:

X(height-cm) 174 175 176 177 178 182 183 186 189 193

Y(weight-kg) 61 65 67 68 72 74 80 87 92 95

Ans: In statistics, the Pearson product-moment correlation

coefficient (sometimes referred to as the PMCC, and typically

denoted by r) is a measure of the correlation (linear dependence)

between two variables X and Y, giving a value between +1 and 1

inclusive. It is widely used in the sciences as a measure of the strength

of linear dependence between two variables



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Pearson's correlation coefficient between two variables is defined as

the covariance of the two variables divided by the product of their

standard deviations:

The above formula defines the population correlation coefficient,

commonly represented by the Greek letter (rho). Substituting

estimates of the covariances and variances based on a sample gives

the sample correlation coefficient, commonly denoted r:

An equivalent expression gives the correlation coefficient as the mean

of the products of the standard scores. Based on a sample of paired

data (Xi, Yi), the sample Pearson correlation coefficient is

where

are the standard score, sample mean, and sample standard deviation.

Calculate Karl Pearson coefficient

http://en.wikipedia.org/wiki/Covariancehttp://en.wikipedia.org/wiki/Standard_deviationshttp://en.wikipedia.org/wiki/Statistical_samplehttp://en.wikipedia.org/wiki/Standard_scorehttp://en.wikipedia.org/wiki/Statistical_samplehttp://en.wikipedia.org/wiki/Standard_scorehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Standard_deviationshttp://en.wikipedia.org/wiki/Statistical_samplehttp://en.wikipedia.org/wiki/Standard_scorehttp://en.wikipedia.org/wiki/Statistical_samplehttp://en.wikipedia.org/wiki/Standard_scorehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Covariance


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X (Height-cm X-182=dx dx2 Y(Weight-kg) Y-76 = dy dy2 dxdy

174 -8 64 61 -15 225 120

175 -7 49 65 -11 121 77

176 -6 36 67 -9 81 54

177 -5 25 68 -8 64 40

178 -4 16 72 -4 16 16

182 0 0 74 -2 4 0

183 1 1 80 4 16 4

186 4 16 87 11 121 44

189 7 49 92 16 256 112

193 11 121 95 19 361 209

x = 1813 dx = -7 dx2 = 377 y = 761 dy = 1 dy2 = 1265 dydx = 676

Formula for Karl Pearson Co-efficient of Correlation.

676/10 (-7/10X1/10)

r = _________________________________

377/10 (-7/10) X 1265/10 (1/10)

67.6 (-0.70 x 0.10)

= _________________________ 37.70 - (-0.70) x 126.50 (0.10)

67.60 + 0.07

= _____________________

37.70 - 0.49 x 126.50 0.01

68.30

= 6.10 x 11.247



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67.6700

= 68.6067

= 0.9863

Karl Pearson Coefficient = 0.9863

End

mb0034 assignment

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