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Statistics for Management

Prof. P. Raj Kumar

ISBN-9789351635819

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AUC2015/MBA/1/01

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MBA, First Semester, Anna University Chennai
Syllabus
 
BA7102: STATISTICS FOR MANAGEMENT
 
Unit-I: Introduction                                                                                                                                                 (12)
Statistics – Definition, Types. Types of Variables – Organising Data - Descriptive Measures. Basic Definitions and Rules for Probability, Conditional Probability Independence of Events, Baye’s Theorem, and Random Variables, Probability Distributions: Binomial, Poisson, Uniform and Normal Distributions.
 
Unit-II: Sampling Distribution and Estimation                                                                                                      (12)
Introduction to Sampling Distributions, Sampling Distribution of Mean and Proportion, Application of Central Limit Theorem, sampling techniques. Estimation: Point and Interval Estimates for Population Parameters of Large Sample and Small Samples, Determining the Sample Size.
 
Unit-III: Testing of Hypothesis – Parametric Tests                                                                                              (12)
Hypothesis Testing: One Sample and Two Sample Tests for Means and Proportions of Large Samples (z-Test), one Sample and Two Sample Tests for Means of Small Samples (t-Test), F-Test for Two Sample Standard Deviations. ANOVAOne and Two Way.
 
Unit-IV: Non-Parametric Tests                                                                                                                              (12)
Chi-Square Test for Single Sample Standard Deviation. Chi-Square Tests forIndependenceof Attributes and Goodness of Fit. Sign Test for Paired Data. Rank Sum Test. Kolmogorov-Smirnov – Test for Goodness of Fit, Comparing Two Populations. Mann – Whitney U Test and Kruskal Wallis Test. One Sample Run Test, Rank Correlation.
 
Unit-V: Correlation, Regression and Time Series Analysis                                                                                 (12)
Correlation Analysis, Estimation of Regression Line. Time Series Analysis: Variations in Time Series, Trend Analysis, Cyclical Variations, Seasonal Variations and Irregular Variations, Forecasting Errors.
Contents 
 
Unit 1: Introduction to Statistics, Probability and Probability Distribution
1.1.       Statistics
9
1.1.1.    Introduction
9
1.1.2.    Meaning of Statistics
9
1.1.3.    Definition of Statistics
9
1.1.4.    Types of Statistics
11
1.1.5.    Importance of Statistics
11
1.1.6.    Limitations of Statistics
12
1.2.       Organising Data
12
1.2.1.    Raw Data
12
1.2.2.    Variable
13
1.2.3.    Types of Variables
13
1.2.4.    Methods of Organising Data
13
1.2.4.1. Statistical Table
14
1.2.4.2. Rank Order
15
1.2.4.3. Frequency Distribution
15
1.2.5.    Descriptive Measures
20
1.3.       Probability
21
1.3.1.    Basic Definition
21
1.3.2.    Characteristics of Probability
21
1.3.3.    Counting Rule of Probability
21
1.4.       Important Terms
22
1.4.1.    Experiment
22
1.4.2.    Random Experiment
22
1.4.3.    Trial and Events
22
1.4.4.    Sample Space
23
1.4.5.    Discrete Sample Space
23
1.4.6.    Complementary Events
23
1.4.7.    Favorable and Unfavorable Events
23
1.4.8.    Mutually Exclusive Events
23
1.4.9.    Mutually Exhaustive Events
24
1.4.10.  Equally likely Events
24
1.4.11. Independenceand Dependence of Events
24
1.4.12.  Odds Against and Odds in Favour
24
1.4.13.  Simple Problem Based on Sample Space
25
1.5.       Assigning Probabilities
27
1.5.1.    Objective Probability
27
1.5.2.    Subjective Probability Approach
29
1.5.3.    Axiomatic Approach
29
1.6.       Rules for Probability
30
1.6.1.    Basic Relationships of Probability
31
1.6.2.    Complement of an Event
31
1.6.3.    Combining Events
31
1.6.3.1. Addition Theorem of Probability
32
1.6.3.2. Multiplication Theorem of Probability
36
1.7.       Marginal Probability
38
1.8.       Conditional Probability
39
1.9.       Bayes’ Theorem
43
1.9.1.    Need of Baye’s Theorem
44
1.9.2.    Applications of Baye’s Theorem
44
1.10.     Probability Distribution
46
1.10.1.  Introduction
46
1.10.2.  Application of Probability Distribution
46
1.10.3.  Random Variable
47
1.10.4.  Probability Mass Function
47
1.10.5.  Probability Density Function
48
1.10.6.  Types of Probability Distribution
48
1.10.6.1.           Binomial Distribution
48
1.10.6.2.           Poisson Distribution
53
1.10.6.3.           Uniform Probability Distribution
57
1.10.6.4.           Normal Probability Distribution
61
1.11.     Exercise
66
 
 
Unit 2: Sampling Distribution and Estimation
2.1.       Sampling
69
2.1.1.    Concept and Definitions
69
2.1.2.    Basic Terminologies of Sampling
69
2.1.3.    Census versus Sample
69
2.1.4.    Advantages of Sampling
70
2.1.5.    Disadvantages of Sampling
70
2.2.       Sampling Techniques
70
2.2.1.    Probability Sampling
70
2.2.2.    Non- Probability Sampling
76
2.2.3.    Criteria for Selection of Probability and Non-         Probability Sampling
79
2.3.       Sampling and Non-Sampling Errors
80
2.3.1.    Sampling Errors
80
2.3.2.    Non-Sampling Errors
80
2.4.       Sampling Distributions
81
2.4.1.    Introduction
81
2.4.2.    Concept of a Sampling Distribution
81
2.4.3.    Properties of Sampling Distribution
82
2.4.6.    Standard Errors
83
2.5.       Central Limit Theorem
84
2.5.1.    Introduction
84
2.5.2.    Application of Central Limit Theorem
85
2.6.       Statistical Inference
87
2.7.       Statistical Estimation
87
2.7.1.    Estimator and Estimate
88
2.7.2.    Type of Estimation
89
2.7.3.    Point Estimation
89
2.7.4.    Interval Estimation
91
2.8.       Sample Size
102
2.8.1.    Introduction
102
2.8.2.    Determining the Sample Size
102
2.8.3.    Determining the Sample Size (n) when      Estimating the Population Mean
102
2.8.4.    Determining the Sample Size (n) When     Estimating the Population Proportion
104
2.9.       Exercise
105
 
 
Unit 3: Testing of Hypothesis: Parametric Tests
3.1.       Testing of Hypothesis
106
3.1.1.    Introduction
106
3.1.2.    Hypothesis Decision Table
106
3.1.3.    Procedure of Testing Hypothesis
107
3.1.4.    Element of Hypothesis Testing
107
3.1.5.    Advantages of the Tests of Hypothesis
108
3.1.6.    Disadvantages of the Tests of Hypothesis
108
3.2.       Important Terms
109
3.2.1.    Null Hypothesis
109
3.2.2.    Alternative Hypothesis
109
3.2.3.    Rejection Region
109
3.2.4.    Errors in Hypothesis Testing
110
3.2.5.    Level of Significance
110
3.2.6.    Degree of Freedom
111
3.2.7.    One Tailed and Two Tailed Tests
111
3.2.8.    P- Value
112
3.3.       Types of Hypothesis Testing
112
3.4.       Hypothesis Testing For Large Sample
114
3.4.1.    Z-test
115
3.4.1.1. Applications of Z Test
117
3.4.1.2. Hypothesis Testing for One Mean of One Sample
117
3.4.1.3. Two-tailed Test for Difference between    Means of Two Samples
118
3.4.1.4. Hypothesis Testing for One Proportion (p) of        One Sample
120
3.4.1.5. Hypothesis Testing for Two Proportions (p1          versus p2) of Two Samples
121
3.4.1.6. Hypothesis Testing for Two Standard       Deviations of Two Samples
121
3.4.1.7. Standard Error of the Difference between Two     Standard Deviation
122
3.5.       Test of Significance for Small Sample
128
3.5.1.    The Assumption of Normality
128
3.5.2.    Size of Samples and Standard Measures
128
3.5.3.    Student’s t – Distribution
128
3.5.3.1. Properties of t - Distribution
129
3.5.3.2. Assumption for Student’s t-test
129
3.5.3.3. Applications of t- Distribution
130
3.5.4.    F-Test
137
3.5.4.1. Assumptions of F-test
138
3.5.4.2. Applications of F-Test
138
3.5.5.    Difference between Large Sample and Small         Sample
139
3.6.       Analysis of Variance (ANOVA)
140
3.6.1.    Characteristics of Analysis of Variance     (ANOVA)
140
3.6.2.    Assumptions of Analysis of Variance        (ANOVA)
140
3.6.3.    Applications of ANOVA
142
3.6.4.    Basic Principle of ANOVA
142
3.6.5.    ANOVA Techniques
142
3.6.6.    Analysis of Variance for One-way            Classification
143
3.6.7.    Analysis of Variance for Two-way           Classification
150
3.7.       Exercise
159
 
 
Unit 4: Non-Parametric Tests
4.1.       Non-Parametric Tests
160
4.1.1.    Introduction
160
4.1.2.    Assumptions about Non-Parametric Test
161
4.1.3.    Difference between Parametric and Non-  Parametric Test
161
4.1.4.    Sign Test for Paired Data
161
4.1.5.    Kolmogorov-Smirnov Test (K-S Test)
163
4.1.5.1. Characteristics of the K-S Test and
163
4.1.5.2. Limitations of the K-S Test
163
4.1.5.3. Kolmogorov-Smirnov Test for Goodness of          Fit
163
4.1.5.4. Kolmogorov-Smirnov Test for Comparing            Two Populations
164
4.1.6.    Wilcoxon Signed Rank Test
165
4.1.7.    One Sample Runs Test (Randomness Test)
168
4.1.8.    Rank Sum Test
169
4.1.8.1. Mann-Whitney U Test
169
4.1.8.2. Kruskal-Wallis Test
172
4.1.9.    Rank Correlation
176
4.1.10.  Chi-Square Test (c2)
177
4.1.10.1.           Definition of Chi-Square Test
178
4.1.10.2.           Degrees of Freedom
178
4.1.10.3.           Chi-square Distribution
178
4.1.10.4.           Steps of  Chi-Square Test
179
4.1.10.5.           Conditions for Applying Chi-Square Test
179
4.1.10.6.           Uses of Chi-Square Test
179
4.1.10.7.           Precautions for using Chi-Square Test
180
4.2.       Exercise
191
 
 
Unit 5: Correlation, Regression and Time Series Analysis
5.1.       Correlation Analysis
193
5.1.1.    Meaning and definition
193
5.1.2.    Uses of Correlation
193
5.1.3.    Types of Correlation
193
5.1.4.    Degree of Correlation
194
5.1.5.    Correlation Coefficient
195
5.2.       Methods of Computing Correlation
195
5.2.1.    Karl Pearson’s Coefficient of Correlation
195
5.2.1.1. Characteristics of Karl Pearson’s Coefficient         of Correlation
195
5.2.1.2. Advantages of Karl Pearson’s Coefficient of          Correlation
196
5.2.1.3. Disadvantages of Karl Pearson’s Coefficient          of Correlation
196
5.2.1.4. Calculation of Karl Pearson Coefficient of             Correlation
196
5.2.2.    Spearman’s Rank Correlation
201
5.3.       Regression Analysis
204
5.3.1.    Introduction
204
5.3.2.    Meaning of Regression
204
5.3.3.    Uses of Regression analysis
204
5.3.4.    Difference between Correlation & Regression        Analysis
205
5.3.5.    Lines of Regression
205
5.3.6.    Regression Equations
206
5.3.7.    Regression Coefficients
206
5.3.8.    Properties of Regression Coefficients
206
5.3.9.    Estimation of Linear Regression Equation
207
5.4.       Relationship between Correlation and        Regression Coefficients
217
5.5.       Time Series Analysis
220
5.5.1.    Introduction
220
5.5.2.    Definition of Time Series
220
5.5.3.    Objectives of Time Series
220
5.5.4.    Models of Time Series
220
5.5.5.    Variations in Time Series
221
5.5.5.1. Secular Variations or Trend (T)
221
5.5.5.2. Seasonal Variations (S)
222
5.5.5.3. Cyclical Variations (C)
222
5.5.5.4. Irregular Variations (I)
223
5.6.       Trend Analysis/Measurement of Trend
223
5.6.1.    Introduction
223
5.6.2.    Secular Trend or Long Term
223
5.6.3.    Free-Hand (or Graphical) Method
223
5.6.4.    Semi-Average Method
224
5.6.5.    Moving-Averages Method
225
5.6.5.1. Odd Period of Moving Average
225
5.6.5.2. Even Period of Moving Average
228
5.6.5.3. Weighted Moving Average
230
5.6.6.    Least Squares Method
230
5.7.       Forecasting
236
5.7.1.    Advantages of Forecasting
236
5.7.2.    Disadvantages of Forecasting
237
5.7.3.    Methods of Forecasting
237
5.7.4.    Forecasting Errors
237
5.8.       Exercise
239
 
 
Solved Paper – 2011
244
Solved Paper – 2012
254
Solved Paper – 2013
261
Classification
270

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Statistics for Management

Statistics for Management

Prof. P. Raj Kumar

ISBN-9789351635819

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