Download MBA 702 (Fall 2011)

MBA 702 (Fall 2011)
Statistical Analysis
Semester Outline
Professor Daneshvary
Chapters 1 and 2 and sections 7.1 and 7.2 of Chapter7: Introduction, Data Collection and
Organizing and Visualizing Data Tabular and Graphical Methods (Descriptive Statistics I):
Objectives: By the end of these chapters, students should understand and be able to:
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Explain key definitions
Describe key data collection methods
Describe different sampling methods
Select a random sample using a random numbers table
Identify types of data and levels of measurement
Describe the different types of survey error
Create an ordered array and a stem-and-leaf display
Construct and interpret a frequency distribution, polygon, and ogive
Construct a histogram
Create and interpret bar charts, pie charts, and scatter diagrams
Present and interpret category data in bar charts and pie charts
Describe appropriate and inappropriate ways to display data graphically
Outline
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I.
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Why Statistics
Basic Concepts
 Population versus sample
 Parameter versus statistic
 Descriptive statistic versus inferential statistic
Sources of Data
Types of Data
Types of Samples
Types of Sampling Methods
 Non probability Samples
 Probability Samples
 With replacement
 Without replacement
Types of Probability Samples
 Simple Random Sample (Using a table of random numbers)
 Systematic Sample
 Stratified Sample
 Cluster Sample
Evaluation of Survey
Dealing with Large Quantitative Data Set
 Raw data
 Ordered array data
 The Stem-and-Leaf Display
Descriptive Summary Measures from A Population
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K.
Quantitative Data Presentation
 The frequency distributions
 The relative and percentage frequency distributions
 Grouping the data
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Histograms
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Polygons
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Cumulative polygons (Ogive)
Qualitative Data Presentation
 Bar, Pie, Pareto Diagram
 The cross-classification (contingency) tables
L.
Chapter 3: Descriptive Statistics II: Numerical Measures (Quantitative Data)
Objectives: By the end of this chapter, students should understand and be able to:
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Compute and interpret the mean, median, and mode for a set of data
Find the range, variance, standard deviation, and coefficient of variation and know what these
values mean
Apply the empirical rule and the Bienaymé-Chebshev rule to describe the variation of population
values around the mean
Construct and interpret a box-and-whiskers plot
Compute and explain the correlation coefficient
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Outline:
A.
Properties of Quantitative Data
 Location
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Measures of central tendency: mean, median, mode, midrange
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Measures of "non-central" tendency: quartiles, deciles, percentiles
 Dispersion
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Measures of dispersion: range, interquartile range, variance, standard deviation,
coefficient of variation
 Shape
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Symmetrical, skewed
 The Five-Number Summary and the Box-and-Whisker Plot
 The Empirical Rule
Bivariate Data
 Scatter Diagram
 Coefficient of Correlation
B.
Chapter 4: Basic Probability And Probability Distribution
Objectives: By the end of this chapter, students should understand and be able to:
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Explain basic probability concepts and definitions
Use contingency tables to view a sample space
Apply common rules of probability
Compute conditional probabilities
Determine whether events are statistically independent
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Outline:
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Types of Probability
Basic Concepts
 A simple event
 A joint event
 The complement of an event
 Mutually exclusive events
 Exhaustive events
 Sample space
Presentation of Sample Space (Contingency table or cross classification)
Rules for Obtaining Probabilities
 Simple or marginal probability rule
 Joint probability (General addition rule)
 Conditional probability
 Multiplication rule
 Statistical independence
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D.
Chapter 5: Some Discrete Probability Distributions
Objectives: By the end of this chapter, students should understand and be able to:
 Interpret the mean and standard deviation for a discrete probability distribution
 Use the binomial probability distribution to find probabilities
 Describe when to apply the binomial distribution
Outline:
A.
Probability Distribution of a Discrete Random Variable
 Concepts
 Mathematical expectations (mean, variance, and standard deviation)
Probability Distributions Functions for Discrete Random Variables
 Binomial distribution (categorical data)
 Process
 Mathematical model
 Mean, standard deviation, and shape
B.
Chapters 6 and 7: The Normal Distribution and Sampling Distribution (Numerical) Data
Objectives: By the end of this chapter, students should understand and be able to:
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Describe the characteristics of the normal distribution
Translate normal distribution problems into standardized normal distribution problems
Find probabilities using a normal distribution table
Evaluate the normality assumption
Define the concept of a sampling distribution
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Determine the mean and standard deviation for the sampling distribution of the sample mean, X
Outline:
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The Probability Density Function of Continuous Distributions, (basic concept)
B.
The Normal Distribution
 Properties
 Mathematical model
 The Standard Normal distribution (Z-distribution)
 Application of the Standard Normal distribution
 Probability Plot
 Uniform distribution
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Sampling Distributions, The Concept
Sampling distribution of the mean
 Properties (Assumption)
 Standard error of the mean
 Distribution of samples mean
i. from a normal population
ii. from nonnormal populations (The Central Limit Theorem)
Chapter 8: Outline For Confidence Interval Estimation (Numerical Data)
Objectives: By the end of this chapter, students should understand and be able to:
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Distinguish between a point estimate and a confidence interval estimate
Construct and interpret a confidence interval estimate for a single population mean using both the Z and t
distributions
Determine the required sample size to estimate a mean within a specified margin of error
Outline:
A.
Confidence Interval Estimation of the Mean
 When standard deviation is known (Z-distribution)
 When standard deviation is unknown (t-distribution)
i. the use of alpha
ii. degrees of freedom
iii. properties of the t-distribution
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Sample size determination for the mean
Chapter 9: The Fundamental of Hypothesis Testing (One-Sample Test)
Objectives: By the end of this chapter, students should understand and be able to:
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Formulate null and alternative hypotheses for applications involving a single population mean
Formulate a decision rule for testing a hypothesis
Know how to use the critical value and p-value approaches to test the null hypothesis
Know what Type I and Type II errors are
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Outline:
A.
Introduction to Hypothesis Testing
 Concept
 Type I and Type II error
 Steps of hypothesis testing
 Examples of hypothesis testing, for the mean of a quantitative variable (Variance
Known)
i. Two-tailed test
ii. One-tailed test
iii. P-value approach
Comparing hypothesis testing with confidence interval estimation
Hypothesis testing, for the mean of a quantitative variable (Variance Unknown)
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Chapter 10: Hypothesis Testing (Two-Sample Tests Numerical data)
Objectives: By the end of this chapter, students should understand and be able to:
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Test hypotheses for the difference between two independent population means (standard deviations known
or unknown)
Use the F table to find critical F values
Complete an F test for the difference between two variances
Outline:
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B.
Introduction and Purpose
Hypothesis Testing for Difference Between the Means of Two Independent Populations with
Equal Variance.
 With known population variance (Z-test)
 With unknown but equal population variance (t-test)
 P-value Approach
 Confidence Interval Estimate
C.
Testing for the Equality of Variances from Two Independent Populations
 Two-tailed (F-test)
 One-tailed (F-test)
Chapter 13: Simple Linear Regression
Objectives: By the end of this chapter, students should understand and be able to:
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Explain the simple linear regression model
Obtain and interpret the simple linear regression equation for a set of data
Evaluate regression residuals for aptness of the fitted model
Understand the assumptions behind regression analysis
Explain measures of variation and determine whether the independent variable is significant
Calculate and interpret confidence intervals for the regression coefficients
Use the Durbin-Watson statistic to check for autocorrelation
Form confidence and prediction intervals around an estimated Y value for a given X
Recognize some potential problems if regression analysis is used incorrectly
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Outline:
A. Introduction and Purpose
B. Steps to:
 The Scatter Diagram and types of relationships
 Determining a simple Linear Regression Model
 The Least-Squares Method
 Interpretation of Slope and Intercept
 Prediction of the Dependent Variable
C. Measures of Variation
 Coefficient of Determination
 Coefficient of Correlation
 The Standard Error of the Estimate
D. Assumptions of Simple Regression and their diagnosis
 Normality of Error
 Homoscedasticity
 Independence of Error
 Durbin-Watson Test for Autocorrelation
E. Inferences about Estimated Parameters
 T-Test for Linear Relationship
 F-Test for the Existence of Relationship (the Model)
 Confidence Interval Test for Slope
 T-Test for a Correlation Coefficient
F. Pitfalls in Regression
Chapter 14: Multiple Linear Regression
Objectives: By the end of this chapter, students should understand and be able to:
 Apply multiple regression analysis to business decision-making situations
 Analyze and interpret the computer output for a multiple regression model
 Perform residual analysis for the multiple regression model
 Test the significance of the independent variables in a multiple regression model
 Use a coefficient of partial determination to test portions of the multiple regression model
 Incorporate qualitative variables into the regression model by using dummy variables
 Use interaction terms in regression models
Outline:
A. Developing a Multiple Regression
 Net Regression Coefficient – Interpretation
 Predicting the Dependent Variable
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Coefficient of Multiple Determination, R2 and Adjusted R2
Assumptions
Significance Test of the Model – F-Test
Hypothesis Test of Individual Parameters
Testing for the contribution of a single variable while other variables are included
Use of Dummy Variable for Categorical Information
B. Interpretation
C. Interaction Term
Chapter 15: Multiple Regression Model Building
Objectives: By the end of this chapter, students should understand and be able to:
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Use quadratic terms in a regression model
Use transformed variables in a regression model
Interpret the estimated coefficients from the transformed variables
Measure the correlation among the independent variables
Outline:
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The Quadratic Regression
Transformation – Linear and Non Linear
Stepwise Regressions
Multicollinearity
Chapter 16: Outline For Time-Series Analysis (if Time allows)
 Business Forecasting, Introduction
 Component Factors – Multiplicative Time-Series Model
 Least-Square Trend Forecasting
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