Statistics with Economics and Business Applications

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Statistics with Economics and Business Applications. Chapter 1 What is Statistics? Inference process, population, sample . The Importance of Statistics. Statistics is the science of collecting, organizing, analyzing and interpreting numerical facts which we call data.

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### Statistics with Economics and Business Applications

Chapter 1 What is Statistics?

Inference process, population, sample

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.

• 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
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.

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?

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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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

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 Inferencemakes use of information from a sample to draw conclusions about the population from which the sample was taken.
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.

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.
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.
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.
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.

POPULATION

SAMPLE

Step 1

x x x

x x x xx

x x xx

xx x x x x x

x x

x x x x x

xx

xxx

QUESTION

Step 2

Step 3

Step 4

xx

xxx

Measure VARIABLES

on Sample units

Step 5

• Make an INFERENCE
• Estimate parameters
• Test hypotheses
• Make a SUMMARY of Sample
• Measurements
• Use graphs such as histogram and
• stem-and-leaf plot
• B) Use numbers called statistics such
• as sample mean, median, variance

Step 6

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.

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.
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?
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 decision-making process.
• Determine the error in a prediction or uncertainty in a decision.
Summary

I. What’s in this lecture?

1. inference process

2. population and samples

II. What's in next lecture?

Descriptive Statistics.