Research SEM2 Reserach Methadology SEM2.pdf

SEM2Reserach Methadology SEM2.

1. 1. Exploratory Research Design
Ans. Exploratory research design is a flexible research method used to gain a better understanding of
a new or poorly understood issue. It is a preliminary step that helps define the research problem and
develop more precise research questions for future, more in-depth studies. Exploratory research is
used when there is little or no existing research on a topic, or when the topic is complex and not well-
defined. It is a valuable tool for generating new ideas, getting insights from different perspectives, and
identifying potential areas for further investigation.
2. Comparison between descriptive research and causal research.
descriptive research causal research
 Descriptive research aims to describe
characteristics of a population or phenomenon. It
seeks to answer questions about who, what, where,
and how many.
Causal research seeks to determine whether
changes in one variable directly cause changes in
another variable
It explores and provides a snapshot or overview of
the subject under study
It aims to explain why certain outcomes occur by
identifying cause-and-effect relationships.
Relies on observation, surveys, and case studies to
gather data.
Typically involves experiments or quasi-
experiments where researchers manipulate
variables to observe their effect on other
variables.
Primarily involves summarizing and describing
data using statistical measures such as averages,
percentages, and frequencies.
Uses statistical techniques to establish
correlations and infer causation, such as
regression analysis or ANOVA.
Conducting a survey to understand the
preferences of customers regarding a product
without trying to influence their choices.
Testing the impact of a new training program on
employee productivity by randomly assigning
employees to either participate in the program or
not, and then measuring their performance.

3. Discuss various types of research
Ans Basic Research (Pure Research)
 Purpose: Basic research aims to expand knowledge and understanding of fundamental principles,
without any immediate or specific application.
 Example: Studying the behaviour of subatomic particles in physics or investigating the genetic basis of
diseases in biology.
2. Applied Research
 Purpose: Applied research aims to solve specific practical problems or answer specific questions
directly related to improving processes, products, or practices.
 Example: Developing new medical treatments based on fundamental biological research or
optimizing manufacturing processes in industry.
3. Quantitative Research
 Purpose: It seeks to quantify relationships, behaviours, or phenomena to generalize findings from a
sample to a larger population.
 Example: Surveys, experiments, and statistical analyses used in fields like sociology, psychology,
economics, and marketing.
4. Qualitative Research
 Purpose: It aims to explore meanings, uncover patterns, and generate theories or hypotheses rather
than testing them.
 Example: Ethnographic studies, case studies, and phenomenological research used in anthropology,
education, and sociology.
5. Mixed Methods Research
 Purpose: It seeks to leverage the strengths of both approaches to triangulate findings and enhance
validity.
 Example: Using surveys to collect numerical data and follow-up interviews to explore participants'
experiences and perspectives.
6. Descriptive Research
 Purpose: Descriptive research aims to describe characteristics of a population or phenomenon. It
focuses on answering questions about who, what, where, and how many.
 Example: Conducting a survey to understand consumer preferences or observing behavior in natural
settings to describe patterns.
7. Exploratory Research
 Purpose: Exploratory research aims to explore a new area or gain initial insights into a phenomenon
where little is known.
 Example: Conducting interviews with experts to understand emerging trends in technology or
investigating early-stage symptoms of a new disease.
8. Explanatory Research
 Purpose: Explanatory research aims to identify factors contributing to a phenomenon or establish
cause-and-effect relationships.
 Example: Testing the impact of a new teaching method on student performance or studying the
relationship between smoking and lung cancer.
4. Compare and contrast between fundamental and applied research.
Fundamental Research Applied Research
comparison Fundamental research focuses on
theoretical knowledge and
understanding
applied research focuses on
practical applications and
problem-solving.
Fundamental research aims to
explore, explain, and understand
natural or social phenomena
applied research aims to solve
specific problems or address
practical issues.
fundamental research often
involves theoretical studies and
controlled experiments
applied research may involve field
trials, simulations, or iterative
testing in real-world settings.
Contrast Fundamental research often has a
longer time frame for results and
applications
applied research focuses on more
immediate applications.

fundamental research may come
from academic institutions,
grants, or foundations interested
in basic science
applied research often attracts
funding from industries,
governments, or organizations
interested in practical outcomes.
Fundamental research may
tolerate more uncertainty and
risk in pursuit of new discoveries,
applied research requires a more
structured approach to validate
practical outcomes.





5. Types of variables and their uses.
Ans. Independent Variables (IV)
 Definition: The independent variable is the variable that is manipulated or controlled by the
researcher. It is the cause or predictor variable.
 Use: Independent variables are used to test the effects they have on dependent variables. They are
crucial for establishing cause-and-effect relationships in experimental and quasi-experimental
research designs.
2. Dependent Variables (DV)
 Definition: The dependent variable is the variable that is measured or observed to determine the
effects of the independent variable. It is the outcome or response variable.
 Use: Dependent variables are used to assess the impact or influence of changes in the independent
variable. They are essential for evaluating the results and conclusions of a study.
3. Control Variables
 Definition: Control variables are variables that are held constant or controlled to prevent them from
influencing the relationship between the independent and dependent variables.
 Use: Control variables help researchers isolate the effects of the independent variable on the
dependent variable by minimizing the influence of other factors.
4. Mediating Variables
 Definition: Mediating variables, also known as intermediary or intervening variables, explain the
relationship between the independent and dependent variables.
 Use: They help clarify the mechanism or process through which the independent variable influences
the dependent variable. Mediating variables are crucial in understanding the underlying mechanisms
of effects.
5. Moderating Variables
 Definition: Moderating variables, also known as interaction variables, influence the direction or
strength of the relationship between the independent and dependent variables.
 Use: They identify conditions under which the relationship between the independent and dependent
variables changes. Moderating variables help determine when and for whom effects are stronger or
weaker.
6. Continuous Variables
 Definition: Continuous variables can take on any value within a certain range. They are measured on a
continuous scale.
 Use: Continuous variables allow for precise measurement and analysis using statistical techniques
such as correlation, regression, and analysis of variance (ANOVA).
6. Significance of Literature review in research.
Ans. A review of literature is significant for several reasons. It provides a comprehensive
overview of existing research and scholarship on a particular topic, helping to establish the
context and significance of the current study or research. It also helps researchers identify gaps
in the existing literature and formulate research questions or hypotheses. Additionally, a review
of literature can help researchers avoid duplicating previous work and build upon the findings of
others. Overall, it is a critical component of academic and scholarly work, providing a foundation
for new research and contributing to the advancement of knowledge in a particular field.




7. Elements of a good research report?
Ans. A good research report is essential for effectively communicating the findings, implications, and
significance of a research study to the intended audience. It should be clear, well-structured, and
organized to facilitate understanding and interpretation of the research outcomes. Here are the key
elements of a good research report:
1. Title Page
 Title: Clearly states the main topic or research question of the study.
 Authors: Names of the researchers involved in the study.
2. Abstract
 Summary: Provides a concise summary of the entire research report.
 Purpose: States the research objectives, methods used, key findings, and conclusions.
3. Introduction
 Objectives: Outlines the specific aims and objectives of the study.
 Significance: Discusses the significance and potential contributions of the study to the field.
4. Literature Review
 Scope: Summarizes and synthesizes relevant literature related to the research topic.
 Theoretical Framework: Provides a theoretical foundation for the study and connects it to existing
theories or conceptual frameworks.
5. Methodology
 Research Design: Describes the overall approach (e.g., experimental, observational, qualitative,
quantitative).
 Data Collection: Explains how data were collected (e.g., surveys, interviews, experiments) and any
instruments used.
 Data Analysis: Describes the methods used to analyse the data (e.g., statistical tests, qualitative
analysis).
6. Results
 Presentation: Presents the findings of the study in a clear and organized manner.
 Data: Includes relevant data, tables, figures, or charts to support the findings.
 Statistical Analysis: Provides statistical analyses conducted and summarizes key findings.
7. Discussion
 Interpretation: Interprets the results in relation to the research question or hypothesis.
 Limitations: Acknowledges any limitations of the study and potential sources of bias.
8. Conclusion
 Summary: Provides a brief summary of the key findings and conclusions drawn from the study.
 Contributions: Highlights the contributions of the study to the field of research.
9. References
 Citations: Lists all sources cited in the report using a consistent citation style (e.g., APA, MLA,
Chicago).
 Accuracy: Ensures accuracy and completeness of references to support the credibility of the research.
10. Appendices
 Supplementary Materials: Includes any additional materials that support the report (e.g.,
questionnaires, raw data, detailed methods).



8. Steps involved in a research process.
Ans. The research process is a systematic approach to conducting research that involves several key
steps. While the specific details may vary depending on the discipline and nature of the research, the
following are generally considered fundamental steps involved in the research process:
1. Identify the Research Problem
 Define the Topic: Select a specific area of interest and narrow down to a well-defined
research problem or question.
 Review Literature: Conduct a thorough review of existing literature to understand what is
already known and identify gaps or areas needing further exploration.
2. Design the Study
 Choose Research Design: Select an appropriate research design (e.g., experimental,
observational, qualitative, quantitative) that aligns with the research objectives and
hypotheses.
 Select Sampling Method: Decide on a sampling technique and determine the sample size
needed to ensure the study's validity and reliability.
 Develop Research Instruments: Design or select tools and instruments for data collection
(e.g., surveys, interviews, experiments) and ensure they are valid and reliable.
3. Collect Data
 Prepare for Data Collection: Set up necessary equipment, tools, or software for data
collection.
 Implement Data Collection: Collect data according to the chosen methods and procedures
while ensuring adherence to ethical guidelines and protocols.
 Monitor Data Quality: Monitor and control for errors or biases during data collection to
maintain data integrity and reliability.
4. Analyse Data
 Organize Data: Organize collected data in a structured format for analysis.
 Apply Statistical or Qualitative Analysis: Depending on the research design and data
collected, apply appropriate statistical techniques or qualitative analysis methods to
examine relationships, patterns, or themes.
5. Draw Conclusions
 Synthesize Results: Synthesize the findings from data analysis and interpretation to address
the research problem or question.
 Discuss Limitations: Reflect on any limitations or constraints encountered during the
research process that may have impacted the findings.
6. Communicate Results
 Write Research Report: Prepare a comprehensive research report that includes all essential
elements such as title, abstract, introduction, methodology, results, discussion, conclusions,
references, and appendices.
 Present Findings: Present the findings through presentations, posters, or publications in
academic journals, conferences, or other relevant forums.




9. Types of Data sources
Ans  Primary Data Sources:
 Surveys and Questionnaires: Data collected directly from individuals or groups through
structured or unstructured questions.
 Experiments: Data obtained from controlled experiments or trials.
 Observations: Data gathered through direct observation of events, behaviors, or conditions.
 Interviews: Data collected through direct interactions, such as face-to-face or phone
interviews.
 Secondary Data Sources:
 Published Research: Data from journals, books, and research papers.
 Government Reports: Data from censuses, economic reports, and other government
publications.
 Corporate Records: Data from business reports, financial statements, and market research.
 Websites and Online Databases: Data from online sources like academic databases,
company websites, and news sites.
 Administrative Data Sources:
 Health Records: Data from hospitals, clinics, and health departments.
 Education Records: Data from schools, colleges, and universities.
 Tax Records: Data from tax filings and revenue agencies.
 Big Data Sources:
 Social media: Data from platforms like Facebook, Twitter, and Instagram.
 Sensor Data: Data from IoT devices, environmental sensors, and smart devices.
 Web Logs: Data from web server logs, clickstreams, and user interactions.
 Geospatial Data Sources:
 GIS Data: Geographic Information System data from maps, satellite images, and spatial
databases.
 Remote Sensing: Data from satellite or aerial imagery used in environmental monitoring and
planning.
 GPS Data: Location data from GPS-enabled devices.
 Qualitative Data Sources:
 Focus Groups: Data from group discussions on specific topics.
 Case Studies: Detailed data from in-depth studies of individual or group cases.
 Textual Data: Data from written documents, transcripts, and narrative content.

10. Significance of using the primary and secondary data and limitations
Ans. Significance of Using Primary Data
Advantages:
1. Specificity: Primary data is tailored to specific research needs and objectives, providing directly
relevant information.
2. Control Over Data Quality: Researchers have control over the data collection process, ensuring high-
quality and reliable data.
3. Timeliness: Primary data is often up-to-date, reflecting current conditions and trends.
4. Uniqueness: This data is unique to the research, which can provide a competitive edge or novel
insights.
Limitations:
1. Costly: Collecting primary data can be expensive due to the resources required for surveys,
experiments, or observations.
2. Time-Consuming: The process of designing, conducting, and analyzing primary research takes a
significant amount of time.
3. Limited Scope: The scope of primary data collection may be limited by geographic, demographic, or
logistical constraints.

2. Significance of Using Secondary Data
Advantages:
1. Cost-Effective: Secondary data is generally less expensive to obtain since it is already collected and
often publicly available.
2. Time-Saving: Using existing data saves time as the data collection process is already completed.
3. Broad Scope: Secondary data can cover extensive geographical areas and large populations, offering a
broader context.
4. Accessibility: Secondary data is readily available from various sources, including government reports,
academic publications, and online databases.
Limitations:
1. Lack of Specificity: Secondary data may not be perfectly aligned with the specific needs and
objectives of the current research.
2. Quality Control Issues: Researchers have no control over the quality and accuracy of the data, which
may vary depending on the source.
3. Outdated Information: Secondary data may not be up-to-date, especially if it was collected long ago.
4. Incomplete Data: The available data may be incomplete or lack necessary details, limiting its
usefulness.
11. Types of charts used in data analysis.
Ans. In data analysis, various types of charts are used to visually represent data, each serving a
specific purpose and providing different insights. Here are some common types of charts:
1. Bar Charts
 Vertical Bar Chart: Displays data with rectangular bars with lengths proportional to the values they
represent. Useful for comparing quantities across different categories.
 Horizontal Bar Chart: Similar to the vertical bar chart but oriented horizontally. Useful when category
names are long.
2. Line Charts
 Simple Line Chart: Plots data points connected by straight lines. Ideal for showing trends over time.
 Multi-Line Chart: Multiple lines represent different data series, useful for comparing trends between
groups.
3. Pie Charts
 Simple Pie Chart: A circular chart divided into sectors, each representing a proportion of the whole.
Useful for showing relative proportions.
 Donut Chart: Similar to a pie chart but with a central hole. Useful for emphasizing parts-to-whole
relationships.
4. Area Charts
 Simple Area Chart: Similar to a line chart, but the area below the line is filled in. Useful for showing
cumulative quantities over time.
12. Comparison between Survey and experiment
SURVEY EXPERIMENT
Survey refers to a technique of gathering information
regarding a variable under study, from the respondents of
the population.
Experiment implies a scientific procedure
wherein the factor under study is isolated to test
hypothesis.
Descriptive Research Experimental Research
Large Relatively small
Social and Behavioral sciences Physical and natural sciences
Field research Laboratory research
Observation, interview, questionnaire, case study etc. Through several readings of experiment.

13. Creation of questionnaire
Ans. Creating an effective questionnaire involves several steps to ensure that the data collected is
valid, reliable, and useful. Here’s a detailed guide on how to create a questionnaire:
1. Define the Purpose
 Identify the Objective: Clearly define what you want to achieve with the questionnaire. What specific
information are you looking to gather?
 Target Audience: Determine who will be answering the questions. Knowing your audience helps tailor
the questions to their level of understanding and interest.
2. Research and Plan
 Review Existing Surveys: Look at similar questionnaires to get an idea of effective question formats
and common pitfalls.
 List Key Topics: Break down your objective into main topics and subtopics to cover all necessary
aspects.
3. Develop Questions
 Types of Questions:
o Open-Ended: Allows respondents to answer in their own words. Useful for detailed insights
but harder to analyze.
o Closed-Ended: Provides specific options (e.g., multiple choice, yes/no, Likert scale). Easier to
analyze but may limit depth.
 Question Wording:
o Clear and Concise: Avoid complex language and keep questions straightforward.
o Neutral: Avoid leading questions that suggest a particular answer.
o Specific: Ensure each question addresses a single concept or issue.
 Question Order:
o Logical Flow: Start with general questions and move to specific ones.
o Grouping: Group related questions together to make the survey easier to follow.
4. Design the Questionnaire
 Format: Choose an appropriate format (online, paper-based, etc.). Ensure it is accessible and easy to
navigate.
5. Pilot Testing
 Pre-Test: Test the questionnaire with a small sample of your target audience to identify any issues.
6. Distribution
 Channels: Choose the best distribution method (email, social media, in-person, etc.) based on your
target audience.
7. Data Collection and Analysis
 Collect Responses: Ensure the data collection process is secure and reliable.
 Analyze Data: Use appropriate statistical methods to analyze the data. Look for trends, patterns, and
significant findings.
8. Reporting Results
 Summarize Findings: Present the data in a clear and concise manner using charts, graphs, and tables.







14. Characteristics of good questionnaire design
Ans. Designing a good questionnaire involves incorporating several key characteristics to ensure that
it effectively collects the desired information while being user-friendly for respondents.
1. Clarity and Simplicity
 Clear Language: Use simple and straightforward language to avoid any confusion. Ensure that the
questions are easily understood by all respondents.
2. Relevance
 Focus on Objectives: Every question should serve a clear purpose related to the research objectives.
Avoid including unnecessary questions that do not add value.
 Targeted Questions: Tailor questions to the specific audience to ensure the responses are relevant
and useful.
3. Conciseness
 Direct Questions: Ask direct questions that require straightforward answers, avoiding long and
complex queries.
4. Logical Flow
 Organized Structure: Arrange questions in a logical order that flows naturally. Group related
questions together in sections.
 Ease of Navigation: Make it easy for respondents to move through the questionnaire without
confusion.
5. Neutrality
 Avoid Leading Questions: Ensure questions are neutrally worded to avoid influencing the
respondent’s answers.
 Balanced Options: Provide balanced response options, especially in closed-ended questions, to avoid
bias.
15. Comparison between Observation and Interview.
Observation Interview
Behavioural and contextual Verbal, subjective experiences and opinions
Natural or controlled environment

Controlled environment
Minimal or no interaction (non-participant) Direct interaction between researcher and
participant
Rich contextual and behavioural data Deep insights into personal experiences
and perceptions
Can be time-consuming, particularly
unstructured
Time-consuming to conduct and transcribe

16. Prepare a questionnaire to assess the service quality of a restaurant in your locality by
using various types of measurement scales.
Ans. Section 1: General Information
1. How often do you visit our restaurant?
o Daily
o Weekly
o Monthly
o Rarely
o This was my first visit
Section 2: Service Quality Assessment
1. How would you rate the quality of our food?
 Very Poor
 Poor
 Neutral
 Good
 Very Good
3. How satisfied are you with the friendliness of our staff?
o Very Dissatisfied
o Dissatisfied
o Neutral
o Satisfied
o Very Satisfied
4. To what extent do you agree with the following statement: "The restaurant's ambiance is
pleasant and welcoming."
o Strongly Disagree
o Disagree
o Neutral
o Agree
o Strongly Agree
2. Semantic Differential Scale 5. Please rate your overall dining experience on the following scales:
 Food Quality: Low Quality ???????????????????? High Quality
 Service Speed: Slow ???????????????????? Fast
 Cleanliness: Very Dirty ???????????????????? Very Clean
 Value for Money: Poor Value ???????????????????? Excellent Value
3. Multiple Choice Questions 6. Which of the following best describes the accuracy of your order?
 Completely accurate
 Mostly accurate
 Somewhat accurate
 Inaccurate
7. How likely are you to recommend our restaurant to others?
o Very Likely
o Likely
o Neutral
o Unlikely
o Very Unlikely
4. Rank Order Scale 8. Please rank the following aspects of our service from most important to least
important to you:
 Quality of food
 Friendliness of staff
 Cleanliness of the restaurant
 Speed of service
 Ambiance of the restaurant
5. Open-Ended Questions 9. What did you like most about your experience at our restaurant?
10. What improvements would you suggest for our restaurant?
6. Demographic Information (Optional) 11. What is your age?
 Under 18
 18-24
 25-34
 35-44
 45-54
 55-64
 65 or older
12. What is your gender?
 Male
 Female
 Non-binary
 Prefer not to say
Conclusion: "Thank you for your valuable feedback. Your responses will help us enhance your future
dining experiences at our restaurant."

17. Formulation of null and alternative hypothesis form a given scenario:
Ans
. You are a restaurant owner who wants to determine if introducing a new menu item (e.g., a
gourmet burger) will increase the average daily sales compared to the current menu.
Formulation of Hypotheses:
Step 1: Define the Variables
 Independent Variable: Introduction of the new menu item (gourmet burger).
 Dependent Variable: Average daily sales.
Step 2: State the Null Hypothesis (H0) The null hypothesis represents the default position that there
is no effect or no difference. It is a statement of no change or no difference and is typically what you
aim to test against.
 H0: Introducing the new menu item will not change the average daily sales.
 Mathematically, if μ0\mu_0μ0 represents the current average daily sales and μ1\mu_1μ1 represents
the average daily sales after introducing the new menu item:
o H0: μ1≤μ0
Step 3: State the Alternative Hypothesis (H1) The alternative hypothesis represents what you are
trying to prove. It is a statement that there is an effect or a difference.
 H1: Introducing the new menu item will increase the average daily sales.
 Mathematically:
o H1: μ1>μ0
Summary of Hypotheses:

Null Hypothesis (H0): The introduction of the new menu item does not increase the average
daily sales (or the average daily sales remain the same or decrease).
o H0: μ1≤μ0

Alternative Hypothesis (H1): The introduction of the new menu item increases the average
daily sales.
o H1: μ1>μ0
18. A teacher claims that the mean score of students in his class is greater than 82 with a
standard deviation of 20. If a sample of 81 students was selected with a mean score of 90
then check if there is enough evidence to support this claim at a 0.05 significance level.
 Ans.

Number of students (sample size),
n
=81


Mean score of the sample,
x
ˉ=90


Population standard deviation,
σ
=20

Significance Level:

α
=0.05

Hypotheses:

Null Hypothesis (
H
0
): The mean score is 82 or less,
μ
≤82
.

Alternative Hypothesis (
H
1
): The mean score is greater than 82,
μ
>82
(right-tailed
test).
Calculation of the Test Statistic (Z-score): Using the formula for the z-score in hypothesis testing:


Substituting the given values:

Critical Value (Z-critical) at
α
=0.05
for a right-tailed test: From standard normal distribution
tables or calculations, the critical z-value for a 0.05 significance level in a right-tailed test is
approximately 1.645.
Decision Rule: If the computed z-score is greater than the critical z-score, we reject the null
hypothesis.
Comparison and Conclusion:

Computed z-score = 3.6

Critical z-score = 1.645
Since 3.6 > 1.645, we reject the null hypothesis.
Interpretation: There is sufficient statistical evidence at the 0.05 significance level to
support the claim that the mean score of students in the math teacher's class is greater than
82.
Final Answers to the Points:

8: The critical or tabular value (TV) is approximately 1.645.

9: The computed value (CV) is 3.6.

10: True, the null hypothesis is rejected.

11: False, there is sufficient evidence to support the teacher's claim.

12: True, the conclusion is that the math teacher's class did perform better than the average
(mean > 82).

19. An online medicine shop claims that the mean delivery time for medicines is less than 120
minutes with a standard deviation of 30 minutes. Is there enough evidence to support this
claim at a 0.05 significance level if 49 orders were examined with a mean of 100 minutes?
Ans.
Given Data:
 Claimed population mean (μ0): 120 minutes
 Sample mean (xˉ): 100 minutes
 Population standard deviation (σ\sigma): 30 minutes
 Sample size (n): 49 orders
 Significance level (α\alphaα): 0.05
Hypotheses:
 Null Hypothesis (H0): μ≥120(The mean delivery time is 120 minutes or more)
 Alternative Hypothesis (H1): μ<120 (The mean delivery time is less than 120 minutes)

Decision Rule:

Determine the critical value for a one-tailed test at α=0.05\alpha = 0.05α=0.05: The critical
value of z for a one-tailed test at the 0.05 significance level is approximately -1.645.

If the calculated z-score is less than the critical value, we reject the null hypothesis.
Conclusion:
 Calculated z-score: -4.66
 Critical value: -1.645
Since -4.66 is less than -1.645, we reject the null hypothesis.

3. 20. A gym trainer claimed that all the new boys in the gym are not equal to 100 kg.A random
sample of thirty boys weight have a mean score of 112.5 kg and the population mean
weight is 100 kg and the standard deviation is 15. Test is at 0.05 significance level.
Ans.
Given Data:
 Claimed population mean (μ0): 100 kg
 Sample mean (xˉ): 112.5 kg
 Population standard deviation (σ): 15 kg
 Sample size (n): 30 boys
 Significance level (α\alphaα): 0.05
Hypotheses:
 Null Hypothesis (H0): μ=100\ (The mean weight of new boys is 100 kg)
 Alternative Hypothesis (H1): μ≠100 (The mean weight of new boys is not equal to 100 kg)

Decision Rule:
 Determine the critical values for a two-tailed test at α=0.05\alpha = 0.05α=0.05: The critical value of z
for a two-tailed test at the 0.05 significance level is approximately ±1.96.
 If the calculated z-score is less than -1.96 or greater than 1.96, we reject the null hypothesis.
Conclusion:

Calculated z-score: 4.56

Critical values: ±1.96
Since 4.56 is greater than 1.96, we reject the null hypothesis.

21. From the data given below obtain the regression equation of X on Y:
X: 2 3 7 9 10
Y: 9 9 10 8 12
Ans.
X=a+bY
Where:

a is the intercept

b is the slope of the regression line
The formulas to calculate the slope (b) and intercept (a) are:


22. properties of correlation coefficient.
Ans.

Some properties of the correlation coefficient are as follows:
1) The correlation coefficient remains in the same measurement as in which the two variables.
2) The sign that correlations of coefficient have will always be the same as the variance.
3) The numerical value of the correlation of coefficient will be between -1 to + 1. It is known as the
real number value.
4) The negative value of the coefficient suggests that the correlation is strong and negative. And if ‘r’
goes on approaching -1, then it means that the relationship is going towards the negative side.
When ‘r’ approaches the side of + 1, then it means the relationship is strong and positive. By this, we
can say that if +1 is the result of the correlation, then the relationship is in a positive state.
5) The weak correlation is signalled when the coefficient of correlation approaches zero. When ‘r’ is
near zero, then we can deduce that the relationship is weak.
6) Correlation coefficient can be very dicey because we cannot say whether the participants are
truthful or not.
The coefficient of correlation is not affected when we interchange the two variables.
7) The coefficient of correlation is a pure number without the effect of any units on it. It also does
not get affected when we add the same number to all the values of one variable. We can multiply all
the variables by the same positive number. It does not affect the correlation coefficient. As we
discussed, ‘r’ is not affected by any unit because ‘r’ is a scale-invariant.




23. Comparison between correlation coefficient and coefficient of determination
correlation coefficient coefficient of determination
Measures strength and direction of linear
relationship
Measures proportion of variance explained
-1 to +1 0 to 1
Indicates direction (positive/negative) and
strength
Indicates explanatory power of the independent
variable(s)
Symmetric: r(X,Y)=r(Y,X)r(X, Y) = r(Y, X)r(X,Y)=r(Y,X) Not symmetric: specific to dependent variable
No (can be negative or positive) Yes (always non-negative)


24. Describe skewness
Ans. Skewness is a measure of the asymmetry of the probability distribution of a real-valued random
variable about its mean. It indicates the degree to which the data deviate from symmetry around the
mean.
1. Definition: Skewness measures the lack of symmetry in a distribution. A symmetric
distribution has zero skewness.
2. Types of Skewness:
o Positive Skewness (Right Skew):
 The tail of the distribution extends towards the right.
 The mean is typically greater than the median, and the mode is less than the
median.
 The distribution is concentrated on the left side and stretched out on the right side.
o Negative Skewness (Left Skew):
 The tail of the distribution extends towards the left.
 The mean is typically less than the median, and the mode is greater than the
median.
 The distribution is concentrated on the right side and stretched out on the left side.
o Zero Skewness:
 The distribution is perfectly symmetric
25. Essential qualities of good sample.
ANS. 1. Representativeness:
 Definition: A good sample accurately represents the characteristics of the population from which it is
drawn.
 Importance: Representativeness ensures that the findings from the sample can be generalized to the
entire population.
2. Randomization:
 Definition: Randomization reduces bias and ensures each member of the population has an equal
chance of being included in the sample.
 Importance: It helps in minimizing the impact of personal bias and ensures that the sample is not
skewed towards specific characteristics of the population.
3. Adequate Size:
 Definition: The sample size should be large enough to provide sufficient statistical power and
precision in estimation.
 Importance: Larger sample sizes reduce sampling error and increase the reliability of the findings.
4. Accuracy:
 Definition: The sample data should accurately reflect the true values of the population parameters
being studied.
 Importance: Accuracy ensures that the conclusions drawn from the sample are valid and reliable.
5. Homogeneity:
 Definition: The sample should consist of units that are similar in relevant characteristics to ensure
consistency in results.
 Importance: Homogeneity reduces variability within the sample and enhances the ability to detect
differences or relationships between variables
26. Types of non-probabilistic sampling techniques.
Ans. non-probabilistic sampling techniques, also known as non-random or non-probability
sampling, do not involve random selection of elements from the population. Instead, elements
are selected based on the judgment or convenience of the researcher. These techniques are
often used in situations where it is difficult to create a complete list of the
1. Convenience Sampling:
 Definition: Convenience sampling involves selecting individuals who are easiest to reach or most
readily available.
 Process: Researchers choose participants based on their accessibility, proximity, or availability.
 Example: Surveying people passing by on the street or using volunteers who are easily accessible.
2. Judgmental or Purposive Sampling:
 Definition: Judgmental sampling involves selecting participants based on the researcher's judgment
or knowledge of the population.
 Process: Researchers select individuals who are believed to be representative of the population based
on specific criteria or characteristics.
 Example: Interviewing experts in a field or selecting participants who fit specific criteria relevant to
the study.
3. Quota Sampling:
 Definition: Quota sampling involves selecting individuals into predefined categories or quotas until
the quota for each category is filled.
 Process: Researchers establish quotas based on specific demographic or other characteristics of
interest.
 Example: Selecting a certain number of participants from different age groups or educational levels
until each quota is met.
4. Snowball Sampling:
 Definition: Snowball sampling involves initially selecting a few participants who meet the criteria for
the study and then asking them to refer others who also meet the criteria.
 Process: The sample grows like a snowball as initial participants refer others, forming a chain of
referrals.
 Example: Studying hard-to-reach populations, such as drug users or minority groups, by asking initial
contacts to refer others.
27. Discuss stratified random sampling
Ans. Stratified random sampling is a type of probability method using which a research organization can
branch off the entire population into multiple non-overlapping, homogeneous groups (strata) and randomly
choose final members from the various strata for research which reduces cost and improves efficiency.
Members in each of these groups should be distinct so that every member of all groups gets an equal
opportunity to be selected using simple probability. This sampling method is also called “random quota
sampling.”
Let’s consider a situation where a research team seeks opinions about religion among various age groups.
Instead of collecting feedback from 326,044,985 U.S citizens, random samples of around 10000 can be
selected for research. These 10000 citizens can be divided into groups according to age, i.e., 18-29, 30-39, 40-
49, 50-59, and 60 and above. Each stratum will have distinct members and the number of members—age,
socioeconomic divisions, nationality, religion, educational achievements, and other classifications.








28. Cluster sampling
Ans. Cluster sampling is a type of sampling method used in statistics and research where the
population is divided into groups, or clusters, and a random sample of these clusters is selected.
Unlike stratified sampling where the population is divided into homogeneous subgroups (strata),
cluster sampling divides the population into heterogeneous clusters that ideally mirror the
characteristics of the entire population.
How Cluster Sampling Works:
1. Define the Population: Identify and define the population of interest. This could be a
geographical area, organizational units, schools, households, etc.
2. Create Clusters: Divide the population into clusters or groups. Clusters should ideally be
heterogeneous but internally homogeneous in terms of the variables of interest.
3. Random Selection of Clusters: Randomly select a certain number of clusters from the
population. This is typically done using simple random sampling techniques or by using a
systematic sampling approach.
4. Include All Units in Selected Clusters: Include all units (individuals, households, etc.)
within the selected clusters in the sample. This step distinguishes cluster sampling from
stratified sampling, where only a subset of individuals from each stratum is sampled.
29. Primary scales of measurement.
Ans. There are four primary scales of measurement, each with its unique properties and levels of
measurement. These scales are crucial as they determine the type of statistical analysis that can be
performed on the data. The four primary scales of measurement are:
1. Nominal Scale:
 Definition: The nominal scale is the simplest level of measurement where variables are categorized
into non-numeric categories or names.
 Characteristics:
o Variables are qualitative and cannot be ranked or ordered.
o Categories are mutually exclusive and exhaustive.
o Examples: Gender (male, female), marital status (single, married, divorced), race/ethnicity
(Asian, Hispanic, Black).
2. Ordinal Scale:
 Definition: The ordinal scale categorizes variables into ordered levels or ranks.
 Characteristics:
o Variables can be ranked or ordered, but the differences between ranks are not uniform.
o There is no assumption of equal intervals between ranks.
o Examples: Educational attainment (high school diploma, bachelor's degree, master's degree),
Likert scales (strongly agree, agree, neutral, disagree, strongly disagree).
3. Interval Scale:
 Definition: The interval scale measures variables where the distance between each value is equal, but
there is no true zero point.
 Characteristics:
o Variables are measured on a scale with equal intervals between points.
o Zero does not represent the absence of the quantity being measured (arbitrary zero).
o Examples: Temperature measured in Celsius or Fahrenheit, dates (calendar years).
4. Ratio Scale:
 Definition: The ratio scale is the highest level of measurement where variables have all the properties
of interval scales, but with a true zero point.
 Characteristics:
o Variables are measured on a scale with equal intervals between points.
o Zero represents the absence of the quantity being measured (absolute zero).
o Ratio comparisons (multiplicative operations) are meaningful.
o Examples: Height, weight, time in seconds, income.

30. Research Hypothesis in context
Ans, In the context of research, a hypothesis is a specific, testable prediction or statement about the
relationship between variables or the outcome of a study. It forms the basis of empirical research and
guides the investigation by specifying what the researcher expects to find.
Components of a Research Hypothesis:
1. Null Hypothesis (H₀):
o Definition: The null hypothesis states that there is no significant relationship or difference
between variables being studied.
o Symbol: H0H₀H0
o Example: "There is no difference in mean test scores between students who receive tutoring
and those who do not."
2. Alternative Hypothesis (H₁ or Hₐ):
o Definition: The alternative hypothesis contradicts the null hypothesis and suggests that there
is a relationship or difference between variables.
o Symbol: H1H₁H1 or HaHₐHa
o Example: "Students who receive tutoring will have higher mean test scores compared to
those who do not."
Types of Research Hypotheses:
1. Directional Hypothesis:
o Predicts the direction of the relationship between variables.
o Example: "The more hours spent studying, the higher the exam scores will be."
2. Non-directional Hypothesis:
o Does not predict the direction of the relationship; it only states that a relationship exists.
o Example: "There is a relationship between hours spent studying and exam scores."
31. Discuss one tail and two tail tests with respect to hypothesis testing.
Ans. In hypothesis testing, the choice between a one-tail (one-sided) test and a two-tail (two-sided)
test depends on the specific nature of the research question and the directionality of the hypothesis
being tested.
One-Tail Test:
1. Definition:
o A one-tail test examines whether the sample data is significantly greater than or less than a
hypothesized population parameter in a specific direction.
o It focuses on detecting an effect in only one direction (either positive or negative).
2. When to Use:
o Use a one-tail test when there is a specific directional prediction or expectation based on
theory or previous research.
o It is appropriate when the researcher is interested in testing whether a parameter is
significantly greater than (right-tailed test) or less than (left-tailed test) a certain value.
3. Example:
o Research Hypothesis: "The new drug treatment decreases symptoms of the disease."
o One-Tail Test (Right-Tailed): The null hypothesis H0H₀H0 would be μ≤μ0 (no decrease or an
increase), and the alternative hypothesis H1H₁H1 would be μ>μ0 (decrease in symptoms).
4. Critical Region:
o The critical region for a one-tail test is located entirely in one tail of the distribution of
sample means or proportions.
Two-Tail Test:
1. Definition:
o A two-tail test examines whether the sample data is significantly different from a
hypothesized population parameter in any direction.
o It tests for the possibility of effects in both directions (either greater than or less than).
2. When to Use:
o Use a two-tail test when there is no specific directional prediction or when the researcher
wants to test for the possibility of differences in both directions.

4. o It is appropriate when the researcher is interested in whether a parameter differs
significantly from a specified value, without specifying the direction of the difference.
3. Example:
o Research Hypothesis: "There is a difference in mean exam scores between two groups."
o Two-Tail Test: The null hypothesis H0H₀H0 would be μ1=μ2\mu₁ = \mu₂μ1=μ2 (no
difference), and the alternative hypothesis H1H₁H1 would be μ1≠μ2\mu₁ ≠ \mu₂μ1=μ2
(difference exists).
4. Critical Region:
o The critical region for a two-tail test is divided between both tails of the distribution of
sample means or proportions.
Key Differences:
 Directionality: One-tail tests focus on effects in one specific direction (either greater than or
less than), while two-tail tests consider effects in both directions.
 Critical Region: One-tail tests have a single critical region in one tail of the distribution,
whereas two-tail tests have critical regions split between both tails.
 Decision Making: In hypothesis testing, the decision to reject or fail to reject the null
hypothesis depends on where the sample statistic falls relative to the critical region(s) defined
by the test type.
32. Explain the types of errors in testing of hypothesis.
Ans. In hypothesis testing, there are two types of errors that can occur based on the decisions made
regarding the null hypothesis (H₀) and the alternative hypothesis (H₁). These errors are known as Type
I and Type II errors, and they have specific implications for the conclusions drawn from the statistical
analysis.
1. Type I Error (α error, False Positive):
 Definition: A Type I error occurs when the null hypothesis (H₀) is rejected, but in reality, the null
hypothesis is true.
 Probability: Denoted by α\alphaα, the significance level of the test, which represents the probability
of rejecting the null hypothesis when it is actually true.
 Consequences: It means concluding there is a significant effect or difference when none exists.
 Example: Concluding that a new drug is effective (rejecting H₀) when it actually has no effect (H₀ is
true).
2. Type II Error (β error, False Negative):
 Definition: A Type II error occurs when the null hypothesis (H₀) is not rejected, but in reality, the
alternative hypothesis (H₁) is true.
 Probability: Denoted by β\betaβ, the probability of failing to reject the null hypothesis when the
alternative hypothesis is true.
 Consequences: It means failing to detect a real effect or difference that actually exists.
 Example: Failing to conclude that a new treatment is effective (not rejecting H₀) when it actually does
have an effect (H₁ is true).
33. Steps of hypotheses testing
Ans. the general steps involved in hypothesis testing:
1. Formulate the Hypotheses:
 Null Hypothesis (H₀):
o Represents the default position or the hypothesis to be tested.
o Typically states that there is no effect, no difference, or no relationship between variables.
o Denoted as H0H₀H0.
 Alternative Hypothesis (H₁ or Hₐ):
o Represents the opposite of the null hypothesis.
o States what the researcher wants to prove or find evidence for.
o Denoted as H1 or Ha.
2. Set the Significance Level (α):
 Definition:
o The significance level (α) is the probability of rejecting the null hypothesis when it is actually true.
o Commonly set at 0.05 (5%) or 0.01 (1%), indicating the acceptable risk of Type I error (false positive).
3. Choose the Appropriate Test Statistic:
 Selection:
o Based on the type of data (e.g., categorical or continuous) and the research question.
o Examples include t-tests, ANOVA, chi-square tests, correlation tests, regression analysis, etc.
4. Collect Data and Calculate the Test Statistic:
 Data Collection:
o Collect a sample that is representative of the population of interest.
 Compute Test Statistic:
o Calculate the appropriate test statistic based on the chosen statistical test.
o This involves applying a formula specific to the chosen test to the sample data.
5. Determine the Critical Region (Rejection Region):
 Definition:
o The critical region is the range of values of the test statistic that leads to rejection of the null
hypothesis.
o Determined based on the chosen significance level (α) and the distribution of the test statistic.
6. Compare the Test Statistic with Critical Value:
 Decision Rule:
o Compare the computed test statistic with the critical value(s) from the appropriate statistical
distribution (e.g., t-distribution, F-distribution).
o If the test statistic falls within the critical region, reject the null hypothesis.
o If the test statistic does not fall within the critical region, fail to reject the null hypothesis.
7. Draw Conclusions:
 Conclusion:
o Based on the comparison:
 Reject H0H₀H0: If the test statistic falls in the critical region, conclude that there is enough
evidence to support the alternative hypothesis H1H₁H1.
 Fail to reject H0H₀H0: If the test statistic does not fall in the critical region, conclude that
there is not enough evidence to reject the null hypothesis H0H₀H0.
34. Significance level
Ans. Definition: The significance level is the probability of rejecting the null hypothesis when it
is actually true.
 Symbol: Denoted by α\alphaα, typically set at 0.05 (5%) or 0.01 (1%), although other levels
such as 0.10 (10%) or custom levels may also be used based on the research context and
conventions.
 Purpose: It establishes the standard for decision-making in hypothesis testing. By setting
α\alphaα, researchers define the maximum acceptable probability of making a Type I error
(incorrectly rejecting the null hypothesis).
Practical Application:
1. Critical Region (Rejection Region):
o The critical region is determined based on the chosen significance level α\alphaα and the
distribution of the test statistic.
o It defines the values of the test statistic that would lead to rejection of the null hypothesis if
observed in the sample data.
2. Decision Rule:
o During hypothesis testing, researchers compare the calculated test statistic with critical
values (cut-off points) derived from the chosen significance level.
o If the test statistic falls within the critical region (beyond the critical values), the null
hypothesis is rejected at the specified significance level.
3. Type I Error (False Positive):
o The significance level directly relates to the risk of Type I error.
o A lower significance level (e.g., α=0.01\alpha = 0.01α=0.01) reduces the probability of Type I
error but may increase the risk of Type II error (false negative) if the sample size is
insufficient to detect real effects.

35. Null and alternative hypothesis
Ans. In hypothesis testing, the null hypothesis (denoted as H0) and the alternative hypothesis
(denoted as H1or Ha) are two complementary statements used to make decisions about the population
parameters based on sample data. Here’s a detailed explanation of each:
Null Hypothesis (H₀):
1. Definition:
o The null hypothesis is a statement that suggests there is no significant difference, effect, or
relationship between variables.
o It represents the status quo or a baseline assumption that is assumed to be true unless
evidence suggests otherwise.
o Often denoted as H0H₀H0.
2. Example:
o If a researcher wants to test a new drug's effectiveness:
 H0: "The new drug has no effect on reducing symptoms."
 This hypothesis assumes there is no change or improvement due to the drug.
3. Decision Rule:
o In hypothesis testing, the null hypothesis is typically tested against an alternative hypothesis.
o The decision to reject or fail to reject the null hypothesis is based on the evidence from the
sample data and the chosen significance level α\alphaα.
Alternative Hypothesis (H₁ or Hₐ):
1. Definition:
o The alternative hypothesis contradicts the null hypothesis and suggests that there is a
significant difference, effect, or relationship between variables.
o It represents what the researcher is trying to prove or find evidence for.
o Denoted as H1 or Ha.
2. Example:
o Continuing with the drug example:
 H1H₁H1: "The new drug reduces symptoms significantly."
 This hypothesis suggests that there is a measurable improvement due to the drug.
3. Types of Alternative Hypotheses:
o One-Tailed (Directional): Specifies a direction of the effect (e.g., increase or decrease).
 Example: H1: "The new drug decreases symptoms compared to the placebo."
o Two-Tailed (Non-directional): Specifies that there is a difference but does not specify the
direction.
 Example: H1: "There is a difference in symptoms between the new drug and the
placebo."