Syllabus Statistical Methods

GUJARAT TECHNOLOGICAL UNIVERSITY  

MASTER OF COMPUTER APPLICATION
SEMESTER: III

Subject Name: Statistical Methods(SM)
Subject Code:  630003

Objectives:
•  To develop the ability to compute descriptive statistics including diagrammatic representation and
interpretation
•  To understand the concept of probability and probability distributions
•  To develop the ability to carry out testing of hypothesis on a population based on statistical measures of
samples
•  To be able to carry out simple linear regression analysis
•  To understand time series analysis and its application to forecasting
•  To introduce the concept of non-parametric methods useful particularly for nominal or ordinal data
Prerequisites: None
Contents:
Unit-1: Descriptive Statistics and Correlation                         (15%)
•  Introduction to Statistics; 
•  Applications in Business & Economics; Data: Summarizing Qualitative & Quantitative Data. 
•  Exploratory Data Analysis: The Stem-and-leaf Display; Cross Tabulation & Scatter Diagrams;
•  Measures of location: Mean, Median, Mode, Percentiles, Quartiles; Measures of Variability: Range,
Inter-quartile Range, Variance, Standard Deviation, Coefficient of Variation; 
•  Measures of Distribution Shape, Relative Location and Detecting Outliers;  
•  Exploratory Data Analysis;  Weighted Mean & working with Grouped Data
•  Measures of Association Between Two Variables; Covariance, Correlation;
Unit-2: Probability & Probability Distribution                         (25%)
•  Introduction to Probability; Experiments, Counting, Rules and Assigning Probabilities;  Events and their
Probabilities;
•  Some basic Relationships of Probability
•  Conditional Probability
•  Baye’s Theorem
•  Random Variables: Discrete, Continuous; 
•  Discrete Probability Distributions; Expected Value & Variance; •  Binomial Probability Distribution
•  Poisson Probability Distribution
•  Normal Probability Distribution, Normal Approximation of Binomial Probabilities
•  Exponential Probability Distribution
Unit-3: Sampling, Sampling Distribution & Interval Estimation                    (20%)
•  Simple Random Sampling, Point Estimation
•  Introduction to Sampling Distributions
•  Sampling Distribution of  
•  Sampling Distribution of  
•  Properties of Point Estimation
•  Other Sampling Methods  
•  Population Mean: σ Known, σ Unknown
•  Determining the Sample Size; Population Proportion
Unit-4: Statistical Inference-Testing of Hypothesis & X2 Test chi-square                  (30%)
•  Introduction
•  Test of significance for Large Samples: Difference between Small & Large Samples; 
•  Two-tailed test for Difference between the Means of Two Samples; 
•  Standard Error of the Difference between two Standard Deviations.
•  Tests of significance for Small Samples: The Assumption of Normality; 
•  Students’ t-Distribution; Properties & Applications of t-Distribution; 
•  Testing Difference between Means of Two Samples (Independent Samples; Dependent Samples) 
•  Definition of chi-square; Degrees of freedom; chi-square Distribution; Conditions for Applying 
Chi-square Test; Uses of chi-square Test; Misuse of chi-square Test
Unit-6: Regression, Time Series Analysis & Forecasting                      (10%)
•  Introduction to Regression; Simple linear Regression Model; least Square Method; Coefficient of
Determination; Correlation Coefficient;
•  Model Assumptions; Residual Analysis: Validating Model Assumptions; Outliers and Influential
Observations
•  Using the Estimated Regression Equation for Estimation & Prediction

Note: Formulae may be provided for parametric and non-parametric tests.
Main Reference Book:
1.  Anderson, Sweeney, Williams, “Statistics for business and economics”, 9th edition, Thompson
Publication
2.  S P Gupta, “Statistical Methods”, 30th edition, S Chand
 
Suggested Additional Reading:
1.  J.Susan Milton & Jesse Arnold, “Introduction to Probability & Statistics: Principles & Applications for Engineering & Computing Sciences”
2.  Bharat Jhunjhunwala, “Business Statistics”, first edition, S Chand, 2008
3.  Richard Levin, David Rubin, “Statistics for Management”, 7th edition, PHI
4.  Nabendu Pal, Sahadeb Sarkar, “Statistics-Concepts and Applications”, 2nd edition, PHI
 
Chapter wise Coverage from the main reference book:
Main Reference Book-1:
Unit 1: Ch-1: 1.1, 1.2; Ch-2: 2.1 to 2.4; Ch-3: 3.1 to 3.6
Unit 2: Ch-4: 4.1 to 4.5; Ch-5: 5.1 to 5.5; Ch-6: 6.2 to 6.4
Unit 3: Ch-7: 7.2 to 7.8; Ch-8: 8.1 to 8.4
Unit 6: Ch-14: 14.1 to 14.4; 14.6, 14.8, 14.9;

Main Reference Book-2:
Unit 4: Ch-3 & Ch-4

Accomplishments of the student after completing the course:
  Ability to apply statistical techniques in decision making in solving real-world problems
  Ability to use computers to analyze the data