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4.4.1 Sampling Distribution

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  Module 4 Sampling and Sampling Distributions
  - 4.1 Sampling Process
    4.1 Sampling Process
    
    4.1.1 Sampling Process
  - 4.2 Sampling Methods
    4.2 Sampling Methods
    
    4.2.1 Sampling Methods
  - 4.3 Analysis of Sample Data
    4.3 Analysis of Sample Data
    
    4.3.1 Analysis of Sample Data
  - 4.4 Sampling Distribution
    4.4 Sampling Distribution
    
    4.4.1 Sampling Distribution 4.4.1 Sampling Distribution
    Table of contents
    
    Introduction
    
    Point Estimators and Sampling Distribution
    
    The Concept of Random Sampling
    
    Sampling Distribution of the Sample Mean (x̄)
    
    Practical Implications
    
    Theoretical Foundations
    
    Conclusion
  - 4.5 Central Limit Theorem
    4.5 Central Limit Theorem
    
    4.5.1 Central Limit Theorem
  - 4.6 Sampling Distribution of Proportion
    4.6 Sampling Distribution of Proportion
    
    4.6.1 Sampling Distribution of Proportion
  - 4.7 Distribution of Sample Variance
    4.7 Distribution of Sample Variance
    
    4.7.1 Distribution of Sample Variance
  - 4.8 Properties of Point Estimator
    4.8 Properties of Point Estimator
    
    4.8.1 Properties of Point Estimator
  - 4.9 Sampling Error vs Non sampling errors
    4.9 Sampling Error vs Non sampling errors
    
    4.9.1 Sampling Error vs Non sampling errors
- Module 5 Statistical Inference
  Module 5 Statistical Inference
  - 5.1 Confidence Interval
    5.1 Confidence Interval
    
    5.1.1 Confidence Interval
    
    5.1.2 Examples of Confidence Interval
    
    5.1.3 Effect of Alpha and Sample Size on Confidence Interval
  - 5.2 Confidence Interval for Population Mean
    5.2 Confidence Interval for Population Mean
    
    5.2.1 Confidence Interval for Population Mean
    
    5.2.2 Confidence Interval for Population Mean - 𝜎 Unknown
    
    5.2.3 Examples of Confidence Interval - 𝜎 Unknown
    
    5.2.4 Determining the Sample Size
  - 5.3 Confidence Interval for Proportion
    5.3 Confidence Interval for Proportion
    
    5.3.1 Confidence Interval for Proportion
  - 5.4 Confidence Interval for Variance
    5.4 Confidence Interval for Variance
    
    5.4.1 Confidence Interval for Variance
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    5.5 Hypothesis Testing
    
    5.5.1 Hypothesis Testing - Introduction
    
    5.5.2 Null and Alternative Hypothesis
  - 5.6 Errors in Hypothesis Testing
    5.6 Errors in Hypothesis Testing
    
    5.6.1 Errors in Hypothesis Testing
  - 5.7 Hypothesis Testing for Population Mean
    5.7 Hypothesis Testing for Population Mean
    
    5.7.1 Hypothesis Testing for Population Mean
    
    5.7.2 Summary - Hypothesis Testing for Population Mean
  - 5.8 Hypothesis Testing for Population Proportion
    5.8 Hypothesis Testing for Population Proportion
    
    5.8.1 Hypothesis Testing for Population Proportion
    
    5.8.2 Examples of Hypothesis Testing for Population Proportion
  - 5.9 Hypothesis Testing for Population Variance
    5.9 Hypothesis Testing for Population Variance
    
    5.9.1 Hypothesis Testing for Population Variance
    
    5.9.2 Summary of Hypothesis Testing for Population Variance
- Module 6 Association between Random Variables and Simple Linear Regression
  Module 6 Association between Random Variables and Simple Linear Regression
  - 6.1 Covariance and Correlation
    6.1 Covariance and Correlation
    
    6.1.1 Explaining Covariance
    
    6.1.2 Correlation
    
    6.1.3 Covariance vs Correlation
  - 6.2 Simple Linear Regression
    6.2 Simple Linear Regression
    
    6.2.1 Simple Linear Regression - I
    
    6.2.2 Simple Linear Regression - II
  - 6.3 Application of Steps in Simple Linear Regression
    6.3 Application of Steps in Simple Linear Regression
    
    6.3.1 Application of Steps in Simple Linear Regression
    
    6.3.2 SLR - Coefficient of Determination
    
    6.3.3 SLR - Correlation Coefficient v-s Coefficient of Determination
    
    6.3.4 SLR - Assumptions on Error Term
    
    6.3.5 SLR - Test of Significance
    
    6.3.6 SLR - Residual Analysis
    
    6.3.7 SLR - Test of Significance and Residual Analysis
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    6.4 SLR Application using Excel
    
    6.4.1 SLR - Application using Examples - I
    
    6.4.2 SLR - Application using Examples - II
- Module 7 Multiple Linear Regression I
  Module 7 Multiple Linear Regression I
  - 7.1 Multiple Linear Regression
    7.1 Multiple Linear Regression
    
    7.1.1 Multiple Linear Regression
    
    7.1.2 MLR - OLS
    
    7.1.3 MLR - Coefficient of Determination
    
    7.1.4 MLR - Test of Significance using F-Test and t-Test
    
    7.1.5 MLR - Multicollinearity
    
    7.1.6 MLR - Residual Analysis
    
    7.1.7 MLR - Outliers and Influential Observations
  - 7.2 Recap
    7.2 Recap
    
    7.2.1 Recap
    
    7.2.2 MLR - Application Recap
  - 7.3 Applications using Excel
    7.3 Applications using Excel
    
    7.3.1 Applications with Examples - I
    
    7.3.2 Applications with Examples - II
    
    7.3.3 Applications with Examples - III
    
    7.3.4 Applications with Examples - IV
    
    7.3.5 Applications with Examples - V
  - 7.4 Multiple Linear Regression II
    7.4 Multiple Linear Regression II
    
    7.4.1 MLR - Intercept and OVB
- Module 8 Multiple Linear Regression II
  Module 8 Multiple Linear Regression II
  - 8.1 Introduction to MLR with Categorical Variables
  - 8.1 MLR with Categorical Variables
    8.1 MLR with Categorical Variables
    
    8.1.1 MLR: Categorical Variables
  - 8.2 Interpretation of Coefficients
    8.2 Interpretation of Coefficients
    
    8.2.1 Interpretation of Coefficients
  - 8.3 Examples of Categorical Variables
    8.3 Examples of Categorical Variables
    
    8.3 Examples of Categorical Variables
  - 8.4 Interaction Variables
    8.4 Interaction Variables
    
    8.4 Interactive Variables
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    1.1 Understanding Markets
    
    What is a Market?
    
    Types of Markets
  - 1.2 Introduction to Marketing
    1.2 Introduction to Marketing
    
    The Social View on Marketing
    
    Introducing Maslow’s Hierarchy of Needs
    
    Satisfying Customer Needs and Wants
    
    Simplified Understanding of Marketing
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    1.3 The Value Framework
    
    The Value Framework
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    1.4 The Evolution of Marketing
    
    The Evolution of Marketing
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    1.5 The Marketing Management
    
    The Language of Marketing
    
    1.5.2 Introduction to the Marketing Management
    
    1.5.3 What can be Marketed?
    
    1.5.4 Social Marketing and Relationship Marketing
  - 1.6 Career Options in Marketing
    1.6 Career Options in Marketing
    
    1.6.1 Career options in Marketing
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    1.7 Case Study Coca Cola
    
    1.7.2 Coca Cola - The origin
    
    1.7.3 Coca-Cola's Expansion (Part 1)
    
    1.7.4 The decline of Coca Cola
    
    1.7.5 Coca Cola - Rivalry Begins (Part 1)
    
    1.7.6 Coca Cola Case Study - Defining Value for the Customers
    
    1.7.7 The Rivalry - Coca Cola's downfall
    
    1.7.8 Coca Cola's Revival
    
    1.7.9 Conclusion of the case
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    2.1.1 Identifying Target Market - Coke Ad 1
    
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    2.1.3 Identifying Target Market - Coke Ad 3
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    2.2 Market Segmentation
    
    2.2.1 Understanding STP
    
    2.2.2 Market Segmentation
    
    2.2.3 Differentiated and Undifferentiated Marketing
    
    2.2.4 Niche marketing
    
    2.2.5 Bases of Segmentation
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    2.3 Targeting Market
    
    2.3.1 Targeting Markets
    
    2.3.2 Segment Size and Attrativeness
    
    2.3.3 Targeting Strategies
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  - 3.1 Differentiation
    3.1 Differentiation
    
    3.1.1 The Foundation of Effective Positioning
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    3.2.1 Executing Positioning
    
    3.2.2 Crafting an Impactful Positioning Statement
    
    3.2.3 Mastering Perceptual Mapping
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    3.3 Market Analysis
    
    3.3.1 Beyond STP: Evaluating Market Size for Effective Marketing Strategy Development
    
    3.3.2 Understanding Market Share: Assessing Demand and Analyzing Market Patterns
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    3.4.1 Exploring Corporate Strategy: The Foundation for Effective Marketing Approaches
    
    3.4.2 Unpacking the BCG Matrix
    
    3.4.3 Strategic Planning Essentials
    
    3.4.4 Functioning of the Organizational Strategy
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    3.5.1 Foundations of Marketing Strategy: Concepts, Processes, and Key Elements
    
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    3.6 Case Study Coca Cola
    
    3.6.1 Case Study - Coca Cola
- Module 04 Understanding Consumer Behaviour
  Module 04 Understanding Consumer Behaviour
  - 4.1 Concept of Consumer Behaviour
    4.1 Concept of Consumer Behaviour
    
    4.1.1 Exploring Consumer Behaviour
    
    4.1.2 Delving Deeper into Consumer Behaviour: Understanding the Definition
  - 4.2 Making Purchase Decisions
    4.2 Making Purchase Decisions
    
    4.2.1 Understanding Consumer Roles in Decision-Making
    
    4.2.2 Exploring Consumer Types and Their Influence on Purchase Decisions
  - 4.3 A Detailed Guide to the Consumer Decision Making Process
    4.3 A Detailed Guide to the Consumer Decision Making Process
    
    4.3.1 Need Recognition
    
    4.3.2 Pre-purchase Information Search
    
    4.3.3 Evaluation of Alternatives
    
    4.3.4 The Purchase Decision
    
    4.3.5 Post Purchase Behaviour
  - 4.4 Factors affecting Consumer Behaviour
    4.4 Factors affecting Consumer Behaviour
    
    4.4.1 Decoding Consumer Behaviour: The Factors That Shape Our Choices
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    4.5 Case Study. Kapoors buy a Car
    
    4.5.1 Case Study Kapoors buy a car
    
    4.5.2 Analyzing Family Dynamics in Consumer Decision-Making: The Kapoor Family Case Study
    
    4.5.3 Understanding Individual Contributions in Family Purchase Decisions
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    5.1.1 Introduction to B2B Markets
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    5.2.1 A Comparative Analysis of B2B and B2C Markets
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    5.3.1 Value Proposition in Business Markets
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    5.4 Segmentation in Business Markets
    
    5.4.1 STP in Business Markets
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    5.5 Buying Benefits and Strategies in Business Markets
    
    5.5.1 Buying Benefits and Strategies in Business Markets
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    5.6.1 Purchase Process in Business Markets
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    5.7 Types of Buyers in Business Markets
    
    5.7.1 Types of Buyers in Business Markets
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    5.8 Case study Mediquip
    
    5.8.1 Mediquip Case Study: Navigating the B2B Sales Process
    
    5.8.3 Mediquip Sales Dynamics
- Module 06 Strategizing Products and Services
  Module 06 Strategizing Products and Services
  - 6.1 Product Concept
    6.1 Product Concept
    
    6.1.1 Product - A Conceptual Framework
    
    6.1.2 Classification of Consumer Goods
  - 6.2 Product Line Management
    6.2 Product Line Management
    
    6.2.1 Product Line Management
    
    6.2.2 Product Line Strategies
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    6.3 Branding
    
    6.3.2 Branding : The Conceptual Framework
    
    6.3.3 Roles of a brand
    
    6.3.4 Building strong brands: Equity, Culture & Value
    
    6.3.5 Building strong brand culture
    
    6.3.6 Building effective brand equity
    
    6.3.7 Generating high brand value
    
    6.3.8 Measuring the success of a brand
  - 6.4 Product Life Cycle (PLC)
    6.4 Product Life Cycle (PLC)
    
    6.4.1 Introduction to PLC
    
    6.4.2 Product Life Cycle : Conceptual Framework
    
    6.4.3 Product Introduction Phase
    
    6.4.4 Market Growth Phase
    
    6.4.5 Maturity Phase
    
    6.4.6 Market Decline Phase
  - 6.5 Service Concept
    6.5 Service Concept
    
    6.5.2 Evolution of Services
    
    6.5.3 Defining Services
    
    6.5.4 Product - Service Mix
    
    6.5.5 Characteristics of Service
    
    6.5.6 Service strategy
  - 6.6 Case Study Santoor
    6.6 Case Study Santoor
    
    6.6.2 Santoor's evolution
    
    6.6.3 Santoor's Repositioning Story : Using Ads Journey
- Module 07 Strategizing Pricing and Distribution
  Module 07 Strategizing Pricing and Distribution
  - 7.1 Price Mix
    7.1 Price Mix
    
    7.1.1 Framework of Pricing
    
    7.1.2 The Language of Pricing
    
    7.1.3 Price Setting Process
    
    7.1.4 Methods of Pricing
    
    7.1.5 Price Discrimination
  - 7.2 Distribution Mix
    7.2 Distribution Mix
    
    7.2.2 Distribution Channels
    
    7.2.3 The Language in Distribution
  - 7.3 Intermediaries in Distribution
    7.3 Intermediaries in Distribution
    
    7.3.1 Types of wholesaling intermediaries
    
    7.3.2 Types of Retailing Intermediaries
    
    7.3.3 Functions of Distribution Channels
  - 7.4 Distribution Channel Decisions
    7.4 Distribution Channel Decisions
    
    7.4.1 Channel Length
    
    7.4.2 Channel Breadth
    
    7.4.3 Channel Design Process
    
    7.4.4 Selecting Distribution Channel
    
    7.4.5 Managing Distribution Channels
    
    7.4.6 Horizontal VS Vertical Channels
    
    7.4.7 Omni-Channel and Multi-Channel Retailing
  - 7.5 Retailing
    7.5 Retailing
    
    7.5.1 Introduction to Retailing
    
    7.5.2 Roles and Responsibilities in Retailing
    
    7.5.3 Characteristics of Retailing
    
    7.5.4 Retail Formats
  - 7.6 D'Light Case Study
    7.6 D'Light Case Study
    
    7.6.1 Introduction to D'Light
    
    7.6.2 D'Light Analysis
    
    7.6.3 Market Context for D'Light
    
    7.6.4 Distribution Channels for D'Light
    
    7.6.6 Strategy for D'Light
- Module 08 Strategizing Promotions
  Module 08 Strategizing Promotions
  - 8.6.1 Digital Marketing : An Overview
  - 8.1 Introduction to Promotion
    8.1 Introduction to Promotion
    
    8.1.1 Introduction to Promotion
  - 8.2 Marketing Communications
    8.2 Marketing Communications
    
    8.2.1 Macro Communication
    
    8.2.2 Micro Communication
    
    8.2.3 Tools and Techniques of Effective Communication
    
    8.2.4 Sales Promotions
    
    8.2.5 Developing Effective Ad Campaigns
    
    8.2.6 Ideal Ad Campaigns : Objectives of Ad Communications
    
    8.2.7 Designing Marketing Communications
  - 8.3 Budgeting
    8.3 Budgeting
    
    8.3.1 Budgeting
  - 8.4 Personal Selling
    8.4 Personal Selling
    
    8.4.1 Personal Selling
    
    8.4.2 Sales Process in B2B Market
    
    8.4.3 Sales Process in B2C Market
  - 8.5 Sales Force Management
    8.5 Sales Force Management
    
    8.5.1 Designing Effective Sales Force
    
    8.5.2 Managing the Sales Force

4.4.1 Sampling Distribution

Introduction¶

Overview: This section delves into the concept of sampling distributions and their importance in statistical inference, specifically focusing on the application of point estimators.

Point Estimators and Sampling Distribution¶

Definition: Point estimators like the sample mean (x̄), sample proportion (p̄), and sample standard deviation (s) are used to estimate population parameters from sample data.

The Concept of Random Sampling¶

Random Sampling as an Experiment: Selecting a sample and calculating x̄, p̄, and s can be considered a random experiment where each statistic is a random variable.
Illustration: Repeated sampling from the same population can yield different values for x̄, p̄, and s, demonstrating their nature as random variables.

Sampling Distribution of the Sample Mean (x̄)¶

Sampling Distribution: Refers to the distribution of the sample mean over repeated sampling from the same population.
Characteristics:
Expectation (E[x̄]): The expected value of x̄, which equals the population mean (μ), indicating that x̄ is an unbiased estimator.
Standard Deviation (σ_x̄): Also known as the standard error, calculated as σ/√n, which decreases with increasing sample size.

Practical Implications¶

Estimating Population Parameters:
The sampling distribution allows us to make probabilistic statements about how close x̄ is to μ.
Understanding the spread (standard error) and the central tendency (mean) of the sampling distribution helps in estimating the population mean accurately.

Theoretical Foundations¶

Central Limit Theorem (CLT): If the sample size is large enough, the sampling distribution of the sample mean will be approximately normal, regardless of the population's distribution.
Significance: This theorem underpins many inferential statistics techniques, allowing for the approximation of the sampling distribution's shape, mean, and variability.

Conclusion¶

Application in Business Decisions:
Knowing the properties of the sampling distribution, such as its mean and standard error, enables businesses to make informed decisions based on sample data.
The sampling distribution concept facilitates the estimation of population parameters and helps quantify the uncertainty associated with these estimates.

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