Statistics with Economics and
Business Applications
Chapter 1 What is Statistics?
Inference process, population, sample
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The Importance of Statistics
• Statistics is the science of collecting, organizing,
analyzing and interpreting numerical facts which we
call data.
• Training in the science of statistics is valuable
preparation for a variety of careers.
• Take control of your life.
• We can no more escape data than we can avoid the use
of words. Quote from H.G. Wells about a centry ago:
Statistical thinking will one day be as necessary for
efficient citizenship as the ability to read and write.
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A few headlines
• South coast medium price hits new threshold:
the one million home. 6/26/04, Santa Barbara
News-Press
• 70 Percent Chance That Large Earthquake Will
Strike San Francisco By 2030. 10/15/99,
Geological Survey
• If Hurricane Ivan Hits U.S., 2004 Would Be A
'1 In 50 Year‘ Series Of Storm Events For
Insurance Industry. EQECAT
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Politics
USA Today, 9/4/04
Bush, Kerry differ on strength of economy.
Bush and Kerry both chose Ohio for their stage
at the beginning of the Labor Day weekend,
traditionally viewed as the kickoff for the fall
campaign. "They promised to create 6 million
jobs, and guess what? They're about 7 million
short," said Kerry.
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Politics
Bush seized on new employment numbers
showing 144,000 new jobs were added to payrolls
as evidence of an improving economy. Kerry said
it merely confirmed that the president's term
would probably end with a net loss of jobs, the
first since the Great Depression.
• Which statistics is close to reality?
• What do President Bush and Senator Kerry have
in common?
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Take Control of Your Life
Statistics provides tools that you need in order to react
intelligently to information you hear or read.
• Almost 85% of lung cancers in men and 45% in women are
tobacco-related.
• 4 out of 5 dentists recommend Dentyne
• Condoms are effective 94% of the time.
• Native Americans are significantly more likely to be hit
crossing the streets than are people of other ethnicities.
• People tend to be more persuasive when they look others
directly in the eye and speak loudly and quickly.
• Women make 75 cents to every dollar a man makes when they
work the same job.
• 79.48% of all statistics are made up on the spot.
We are not saying that each one of these claims is true!
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California SupperLotto Plus
Prize Categories and Odds:
Match
All 5 of 5 And Mega
All 5 of 5
Any 4 of 5 and Mega
Any 4 of 5
Any 3 of 5 And Mega
Any 3 of 5
Any 2 of 5 And Mega
Any 1 of 5 And Mega
None of 5, Only Mega
Odds 1 in
41,416,353
1,592,937
197,221
7,585
4,810
185
361
74
49
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Now let us get to work!
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Statistical Inference
• What is Statistics? Statistics is the science of
collecting, organizing, analyzing and
interpreting data in order to make decision in
the presence of uncertainty.
• Statistical Inference makes use of information
from a sample to draw conclusions about the
population from which the sample was taken.
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Population and Sample
• Population The population is the set representing all
measurements of interest to the investigator.
A population is any entire collection of people, animals,
plants or things from which we may collect data. It is
the entire group we are interested in, which we wish
to describe or draw conclusions about.
In order to make any generalizations about a
population, a sample, that is meant to be
representative of the population, is often studied.
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Population and Sample
•
•
•
•
•
A sample is a subset of measurements selected from
the population of interest.
The sample should be representative of the population.
A sample could be the whole population, e.g. US
Census in ideal situations.
In many cases the population is conceptual, e.g. daily
yields of a power plant for next 2 years.
In most cases measuring the whole population is too
costly, unnecessary or impossible.
There are many possible samples when sample is a
subset of the whole population.
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EXAMPLE 1: The President's Approval Rating
A Time Magazine/CNN pool of 1500 adult
American conducted on January 7, 2002 shows
that 618 said the "approve", 702 "disapprove"
and 180 either declined to answer or has no
opinion.
• Population: 150-plus million adult American.
• Sample: 1500 interviewed.
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EXAMPLE 2: Earth/Moon Mass Ratio
The ratio of the mass of the earth to that of the moon
were obtained during several different spacecraft
flights: 81.3001, 81.3015, 81.3006, 81.3011, 81.299,
81.3015, 81.3005, 81.3021. These number differ form
one another (and presumably form the true ratio)
because of measurement error.
• Population: all possible measurements might be
made under similar experimental conditions. It is a
conceptual (hypothetical) population since it does not
actually exist.
• Sample: eight measurements.
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The Six Step Inference Process
• Step 1: What is the QUESTION of interest?
• Step 2: What POPULATION is associated with the
QUESTION?
• Step 3: Take a SAMPLE from the POPULATION.
• Step 4: Measure one or more VARIABLES on each
unit in the Sample.
• Step 5: Make a SUMMARY of all Sample Data
obtained on the VARIABLES.
• Step 6: Make an INFERENCE about the
POPULATION from the Sample Summary.
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POPULATION
Step 1
QUESTION
Step 2
x x x
x x x xx
x
x
xx
xx x x x x x
xxx
x
x x xxx
xxx
SAMPLE
xx
xxx
Step 3
Step 4
Measure VARIABLES
on Sample units
Step 5
Make an INFERENCE
about the population
A) Estimate parameters
B) Test hypotheses
Step 6
Make a SUMMARY of Sample
Measurements
A) Use graphs such as histogram and
stem-and-leaf plot
B) Use numbers called statistics such
as sample mean, median, variance
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EXAMPLE: Pollution at an oil refinery
Environmental Protection Agency (EPA) has accused
Shell Oil Company of violation environmental
regulations at its refinery located in Huston during the
year 2001. The regulations state that the average
petroleum leaked into the ground at the refinery must
not exceed 100 gallons per day during any calendar
year. Fine for violating the regulations is $1,000,000.
EPA regulators visited the refinery on eight days in
December, 2001 and measured the petroleum leaked
in gallons as 110,96,104,101,87,99,116,108.
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EXAMPLE: Pollution at an oil refinery
The Six Step Inference Process:
• Question: Does average leakage exceed 100 gallons
per day?
• Population: Every single day of that year 2001.
• Sample: Measurements on those 8 days in December.
• Variable: Leakage in gallons.
• Summary: Average leakage=102.625 gallon/day.
• Inference: The average leakage for the year
2001exceeds 100 gallons. The company should be
fined.
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EXAMPLE: Pollution at an oil refinery
Follow-up questions:
• Is the sample representative of the population?
• What argument might Shell use to contend that
the EPA's conclusions are unreliable?
• What could EPA administrators do to improve
the statistical techniques?
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The Role of Statistics in Inference Making
• Find efficient design of experiments to
reduce the cost and size of studies.
• Find the best predictor or decisionmaking process.
• Determine the error in a prediction or
uncertainty in a decision.
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Summary
I. What’s in this lecture?
1. inference process
2. population and samples
II. What's in next lecture?
Descriptive Statistics.
Read Chapters 1 and 2.
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