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Statistics with Economics and Statistics with Economics and Business ApplicationsBusiness Applications

Chapter 1 What is Statistics?

Inference process, population, sample

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The Importance of StatisticsThe 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 headlinesA 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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PoliticsPolitics

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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PoliticsPolitics 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 LifeTake 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 PlusCalifornia SupperLotto Plus Prize Categories and Odds:

Match Odds 1 in All 5 of 5 And Mega         41,416,353         All 5 of 5 1,592,937 Any 4 of 5 and Mega 197,221 Any 4 of 5 7,585 Any 3 of 5 And Mega 4,810 Any 3 of 5 185 Any 2 of 5 And Mega 361 Any 1 of 5 And Mega 74 None of 5, Only Mega 49   

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Now let us get to work! Now let us get to work!

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Statistical InferenceStatistical 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 SamplePopulation 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 SamplePopulation 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 RatingEXAMPLE 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 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 ProcessThe 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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x x x x x x xx

x x xx xx x x x x x

x x x x x x x

POPULATION

Step 2

Step 1

xxxxx

xx xxxStep 3

SAMPLE

Measure VARIABLESon Sample units

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

Step 4

Step 5

Make an INFERENCE about the population

A) Estimate parametersB) Test hypotheses

Step 6

QUESTION

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EXAMPLE: Pollution at an oil refineryEXAMPLE: 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 refineryEXAMPLE: 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 refineryEXAMPLE: 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 MakingThe Role of Statistics in Inference Making

• Find efficient design of experiments to reduce the cost and size of studies.

• Find the best predictor or decision-making process.

• Determine the error in a prediction or uncertainty in a decision.

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SummarySummary

I. I. What’s in this lecture?What’s in this lecture?

1. inference process

2. population and samples

II. II. What's in next lecture?What's in next lecture?

Descriptive Statistics.

Read Chapters 1 and 2.