Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/Irwin

Chapter 1

An Introduction to Business Statistics

1-2

Chapter Outline

1.1 Populations and Samples1.2 Selecting a Random Sample1.3 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)

1-3

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

1-4

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

1-5

Population of Measurements

Measurement of the variable of interest for each and every population unitSometimes referred to as an observationFor example, annual starting salaries of all

graduates from last year’s MBA programCensus: The process of collecting the

population of all measurementsSample: A subset of population units

1-6

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

1-7

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 chosenSample with replacementSample without replacement

1-8

Approximately Random Samples

In general, must make a list identifying each and every individual population unitThis may not be possible

Draw a “systematic” sampleRandomly enter the population and

systematically sample every kth unit

1-9

Finite and Infinite Populations

Finite if it is of fixed and limited size

Finite if it can be countedInfinite if it is unlimitedInfinite if listing or counting every

element is impossible

1-10

ProcessInputs Outputs

Sampling a Process

1-11

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

1-12

Runs Plot

Figure 1.2

1-13

Out of Control (Level Decreasing)

Figure 1.3

1-14

Out of Control (Variation Increasing)

Figure 1.4

1-15

1.3 Ratio, Interval, Ordinal, and Nominative Scales of Measurement (Optional)

NominativeOrdinalIntervalRatio

1-16

Qualitative Variables

Nominative: A qualitative variable for which there is no meaningful ordering, or ranking, of the categoriesExample: gender, car color

Ordinal: A qualitative variable for which there is a meaningful ordering, or ranking, of the categoriesExample: teaching effectiveness

1-17

Interval Variable

All of the characteristics of ordinal plus…

Measurements are on a numerical scale with an arbitrary zero pointThe “zero” is assigned: it is nonphysical

and not meaningfulZero does not mean the absence of the

quantity that we are trying to measure

1-18

Interval Variable Continued

Can only meaningfully compare values by the interval between themCannot compare values by taking their

ratios“Interval” is the arithmetic difference

between the valuesExample: temperature

0 F means “cold,” not “no heat”60 F is not twice as warm as 30 F

1-19

Ratio Variable

All the characteristics of interval plus…

Measurements are on a numerical scale with a meaningful zero pointZero 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

1-20

Ratio Variable Continued

In business and finance, most quantitative variables are ratio variables, such as anything to do with moneyExamples: Earnings, profit, loss, age,

distance, height, weight

1-21

1.4 An Introduction to Survey Sampling (Optional)

Already know some sampling methodsAlso called sampling designs, they are:

Random samplingSystematic samplingVoluntary response sampling

But there are other sample designsStratified random samplingMulti-stage cluster sampling

1-22

Stratified Random Sample

Divide the population into non-overlapping groups, called strata, of similar unitsSeparately, select a random sample from

each and every stratumCombine the random samples from each

stratum to make the full sampleAppropriate when the population

consists of two or more different groups

1-23

Multi-Stage Cluster Sampling

Group a population into subpopulationsEach cluster is a representative small-

scale version of the populationPick a random sample of clustersA simple random sample is chosen

from each chosen clusterCombine the random samples from

each cluster to make the full sample

1-24

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

1-25

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

1-26

1.5 More About Data Acquisition and Survey Sampling (Optional)

Web searches…Cheap, fastLimited in type of information we are

able to findData collection agency

Cost moneyBuy subscription or individual reports

1-27

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

1-28

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

1-29

Errors Occurring in Surveys

Random sampling should eliminate bias

But even a random sample may not be representative because of:Sampling errorUnder-coverageNon-responseResponse bias