Chapter 1

Report
Chapter 1
An Introduction to Business
Statistics
McGraw-Hill/Irwin
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
1.1 Populations and Samples
1.2 Selecting a Random Sample
1.3 Ratio, Interval, Ordinal, and Nominative
Scales of Measurement (Optional)
1.4 An Introduction to Survey Sampling
(Optional)
1.5 More About Data Acquisition and Survey
Sampling (Optional)
1-2
1.1 Populations and Samples
Population: A set of existing units
(people, objects or events)
Variable: Any characteristic of the
population
Census: An examination all of the
population of measurements
Sample: A subset of the units of a
population
1-3
Quantitative Versus Qualitative
 Quantitative: Measurements that represent
quantities
 Annual starting salary
 Gasoline mileage
 Qualitative: A descriptive category to which
a population unit belongs: a descriptive
attribute of a population unit
 A person’s gender is qualitative
 Make of automobile
1-4
Population of Measurements
Measurement of the variable of interest
for each and every population unit
 Sometimes referred to as an observation
 For example, annual starting salaries of all
graduates from last year’s MBA program
Census: The process of collecting the
population of all measurements
Sample: A subset of population units
1-5
Descriptive Statistics
Descriptive Statistics: The science of
describing the important aspects of a
set of measurements
Statistical Inference: The science of
describing the important aspects a set
of measurements
1-6
1.2 Selecting a Random Sample
Random Sample: Selected so that, on
each selection from the population,
every unit remaining in the population
on that selection has the same chance
of being chosen
 Sample with replacement
 Sample without replacement
1-7
Approximately Random Samples
In general, must make a list identifying
each and every individual population
unit
 This may not be possible
Draw a “systematic” sample
Randomly enter the population and
systematically sample every kth unit
1-8
Finite and Infinite Populations
Finite if it is of fixed and limited size
Finite if it can be counted
Infinite if it is unlimited
Infinite if listing or counting every
element is impossible
1-9
Sampling a Process
Inputs
Process
Outputs
1-10
Statistical Control
To determine if a process is in control or
not, sample the process often enough
to detect unusual variations
 Issue: How often to sample?
See Example 1.3, “The Car Mileage
Case: Estimating Mileage,” in the
textbook
1-11
Runs Plot
Figure 1.2
1-12
Out of Control (Level Decreasing)
Figure 1.3
1-13
Out of Control (Variation Increasing)
Figure 1.4
1-14
1.3 Ratio, Interval, Ordinal, and
Nominative Scales of Measurement
(Optional)
Nominative
Ordinal
Interval
Ratio
1-15
Qualitative Variables
Nominative: A qualitative variable for
which there is no meaningful ordering,
or ranking, of the categories
 Example: gender, car color
Ordinal: A qualitative variable for
which there is a meaningful ordering, or
ranking, of the categories
 Example: teaching effectiveness
1-16
Interval Variable
All of the characteristics of ordinal
plus…
Measurements are on a numerical scale
with an arbitrary zero point
 The “zero” is assigned: it is nonphysical
and not meaningful
 Zero does not mean the absence of the
quantity that we are trying to measure
1-17
Interval Variable
Continued
Can only meaningfully compare values
by the interval between them
 Cannot compare values by taking their
ratios
 “Interval” is the arithmetic difference
between the values
Example: temperature
 0 F means “cold,” not “no heat”
 60 F is not twice as warm as 30 F
1-18
Ratio Variable
All the characteristics of interval plus…
Measurements are on a numerical scale
with a meaningful zero point
 Zero means “none” or “nothing”
Values can be compared in terms of
their interval and ratio
 $30 is $20 more than $10
 $0 means no money
1-19
Ratio Variable
Continued
In business and finance, most
quantitative variables are ratio
variables, such as anything to do with
money
 Examples: Earnings, profit, loss, age,
distance, height, weight
1-20
1.4 An Introduction to Survey
Sampling (Optional)
Already know some sampling methods
 Also called sampling designs, they are:
 Random sampling
 Systematic sampling
 Voluntary response sampling
But there are other sample designs
 Stratified random sampling
 Multi-stage cluster sampling
1-21
Stratified Random Sample
Divide the population into nonoverlapping groups, called strata, of
similar units
 Separately, select a random sample from
each and every stratum
 Combine the random samples from each
stratum to make the full sample
Appropriate when the population
consists of two or more different groups
1-22
Multi-Stage Cluster Sampling
Group a population into subpopulations
 Each cluster is a representative small-scale
version of the population
Pick a random sample of clusters
A simple random sample is chosen from
each chosen cluster
Combine the random samples from
each cluster to make the full sample
1-23
Combination
 It is sometimes a good idea to combine
stratification with multistage cluster sampling
 For example, we wish to estimate the
proportion of all registered voters who favor a
presidential candidate
 Divide United States into regions
 Use these regions as strata
 Take a multi-stage cluster sample from each
stratum
1-24
Systematic Sampling
To systematically select n units without
replacement from a frame of N units,
divide N by n and round down to a
whole number
Randomly select one unit within the
first N/n interval
Select every N/nth unit after that
1-25
1.5 More About Data Acquisition and
Survey Sampling (Optional)
Web searches…
 Cheap, fast
 Limited in type of information we are able
to find
Data collection agency
 Cost money
 Buy subscription or individual reports
1-26
Initiating a Study
 First, define the variable of interest, called a
response variable
 Next, define other variables that may be
related to the variable of interest and will be
measured, called independent variables
 If we manipulate the independent variables,
we have an experimental study
 If unable to control independent variables,
the study is observational
1-27
Types of Survey Questions
Dichotomous questions ask for a yes/no
response
Multiple choice questions give the
respondent a list of of choices to select
from
Open-ended questions allow the
respondent to answer in their own
words
1-28
Errors Occurring in Surveys
Random sampling should eliminate bias
But even a random sample may not be
representative because of:
 Sampling error
 Under-coverage
 Non-response
 Response bias
1-29

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