INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
CHAPTER TWO
DESCRIPTIVE STATISTICS:
TABULAR AND GRAPHICAL METHODS
CHAPTER OUTLINE AND REVIEW
In Chapter 1, you were introduced to the concept of statistics and in exercise *6 of that
chapter you were given a frequency distribution of the ages of 180 stude
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Kinnari Amin
Conditional Probability and General Multiplication Rule
Objectives:
 Identify Independent and dependent events
 Find Probability of independent events
 Find Probability of dependent events
 Find Conditional probability
 General multiplic
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
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Chapter
4
PROBABILITY
P
lease stand up in front of the class and give your oral report on describing data
using statistical methods. Does this request to speak in front of people in public make
you panic? If s
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Kinnari Amin
Conditional Probability and General Multiplication Rule
Objectives:
 Identify Independent and dependent events
 Find Probability of independent events
 Find Probability of dependent events
 Find Conditional probability
 General multiplic
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Review for TEST 2 STA 2023
FALL 2013
Name_
Find the mean of the data summarized in the given frequency distribution.
1) A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the
mean salary.
Salary ($) Employee
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
SI
Practice material for week 3
Further Topics on Probability
Conditional Probability
The probability of an event B occurring when it is known that some event A has occurred is called a
conditional probability and is denoted by P ( B A). The symbol P ( B
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Practice material for week 1
Q1.
i.
ii.
How many three digit numbers can be formed from the six digits are 0, 2, 3, 5, 6, 7, and 9, when:
Repetitions are allowed?
Repetitions are not allowed or digit used only once.?
Answers the following parts when repet
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Lesson note #
Statistical Inference
Testing of Hypothesis
Type I Error:
Rejection of the null hypothesis when it is true is called a type I error.
Type II Error:
Acceptance of the null hypothesis when it is false is called a type II error.
Decision of the
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Analysis of Variance (ANOVA)
One Way Classification
Random samples of size n are selected from each of k populations. It will be assumed
that the k populations are independent and normally distributed with means
1 2 3 4 . K and common variance 2 . We wish
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
MODEL QUESTION
Q1.
The management of an institute is interested to study the difference between the average
marks of the two different programs. One is 3semester program and other one is 4semester program. The sample data of results of students belongs t
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Lesson Note:
Topic
:
Course
:
Estimation
Statistical Inference
Statistical Inference
The theory of Statistical inference consists of those methods by which one makes
inferences or generalizations about a population. The trend of today is the classical
met
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
SI
Practice material for week 5
Discrete Probability Distribution
Uniform Distribution:
The simplest of all discrete probability distribution is one in which the random variable assumes all its
values with equal probabilities. Such a probability distribut
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
SI
for week 2
Practice material
Set Theory
Set and Element
A set may be viewed as a collection of objects, the elements
or members of the set. Usually the set is represented by
capital English alphabets while its elements is represents by
small alphabets.
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
SI
Practice material for week 4
Random Variable:
Random variable can defined as a function whose value is a real number determined by each element in
the sample space is called a random variable OR a numerical event whose value is determined by a
chance p
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Regression Equation
Regression Equation:
A mathematical equation that allows us to predict values of one dependent variable from
known values of one or more independent variables is called regression equation.
Type of Regression Equation:
There are follow
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Structural Equation Modeling (SEM)
SEM is a comprehensive statistical
approach to testing hypotheses about
relations among observed and latent variables
(Hoyle, 1995).
The set of equations are solved
simultaneously to test model fit and estimate
parameter
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Question 1:
(Marks: 3+5=8)
The fourth mean moment of a symmetric distribution is 243. What would
be the value of the standard deviation in order that the distribution may
be mesokurtic?
Solution:
Standard deviation is equal to 2nd moment.
So that m4 = 24
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
ANOVA
Objective: Comparison of MORE THAN two populations on the basis of
their means
ANalysis Of Variances (Variance within group, Variance among group
and Total Variance)
Step # 1
Ho:
All population means are equal. (1 = 2 = 3 = 4 = 5 = = k)
HA:
Atleast
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
Step 1
Ho:
Population mean =_ or
_
HA:
Population mean _ or
_
Step 2
Level of significance = =_
_ tailed test
Step 3
Test statistic (Z,T,F,.etc)
N = _
X _
S = = _
x
Z cal
_
/ n
Step 4
Critical region
Ztab = _
Step 5
Rejection Rule
lZcall > lZtabl
Step
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
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Spring 2015
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Probability
PART
3
and
Probability
Distributions
CHAPTER 5
Probability
We now take a break from the statistical process. Why? In
CHAPTER 6
Discrete Probability
Distributions
that generalize results obtain
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
32
Measures of Central Tendency and Dispersion
In this section we discuss two important aspects of data which are its center and its spread. The mean, median, and the mode are measures of central tendency that describe where data are centered. The range,
INTRODUCTION TO STATISTICS FOR BUSINESS AND ECONOMICS
ECON 15419

Spring 2015
PROBLEMS
USING COMBINATIONS
AND PROBABILITY
()
License
Plate Problems
Each of the following problems assumes that a state's license plates consist of a certain
numberof lettersfollowedby a certain numberof numbers.
/
1) How many different plates can be ma