Introduction to Probability Introduction to Probability and Statisticsand Statistics

Fourteenth EditionFourteenth Edition

IntroductionIntroduction

Train Your Brain for StatisticsTrain Your Brain for Statistics

What is Statistics?What is Statistics?

What does a statistician do?

Player Games Minutes Points Rebounds FG%Player Games Minutes Points Rebounds FG%BobBob 34 34 32.7 32.7 2424 7.6 .552 7.6 .552AndyAndy 36 36 31.5 31.5 2121 8.4 .465 8.4 .465Larry 30Larry 30 33.0 33.0 1818 5.6 .493 5.6 .493Michael 31Michael 31 35.1 35.1 2929 6.1 .422 6.1 .422

Player Games Minutes Points Rebounds FG%Player Games Minutes Points Rebounds FG%BobBob 34 34 32.7 32.7 2424 7.6 .552 7.6 .552AndyAndy 36 36 31.5 31.5 2121 8.4 .465 8.4 .465Larry 30Larry 30 33.0 33.0 1818 5.6 .493 5.6 .493Michael 31Michael 31 35.1 35.1 2929 6.1 .422 6.1 .422

Job of a StatisticianJob of a Statistician• Collects numbers or data

• Organizes or arranges the data

• Analyzes the data

• Infers general conclusions

Uses of StatisticsUses of Statistics

• a theoretical discipline in its own right

• a tool for researchers in other fields• used to draw general conclusions

in a large variety of applications

POLITICSPOLITICS

• Forecasting and predicting winners

• Where to concentrate

• What should a statistician DO? (Cannot survey on every voter)

If the election for mayor of Los Angeles were held today, If the election for mayor of Los Angeles were held today, who would you be more likely to vote for?who would you be more likely to vote for?

James HahnJames Hahn 32%32%Magic JohnsonMagic Johnson 36%36%Someone elseSomeone else 11%11%

No opinion yetNo opinion yet 21%21%

If the election for mayor of Los Angeles were held today, If the election for mayor of Los Angeles were held today, who would you be more likely to vote for?who would you be more likely to vote for?

James HahnJames Hahn 32%32%Magic JohnsonMagic Johnson 36%36%Someone elseSomeone else 11%11%

No opinion yetNo opinion yet 21%21%

• To market product

• Average length of life of a light bulb?

• What should statistician do? (cannot test all the bulbs)

INDUSTRYINDUSTRY

SolutionSolution• Collect a smaller set of measurements

that will (hopefully) be representative of the whole set.

• POPULATIONPOPULATION:: set of all measurements

• SAMPLESAMPLE:: A subset of population

DefinitionsDefinitionsVariableVariable is a characteristic that changes or varies is a characteristic that changes or varies

over time and/or for different individuals or over time and/or for different individuals or objects under considerationobjects under consideration

Experimental UnitsExperimental Units are are items or objects on which items or objects on which measurements are takenmeasurements are taken

Measurement Measurement results when a variable is actually results when a variable is actually measured on an experimental unitmeasured on an experimental unit

PopulationPopulation is the WHOLE set of all possible is the WHOLE set of all possible measurementsmeasurements

SampleSample is a subset of populationis a subset of population

ExamplesExamples

• Light bulbsLight bulbs

–Variable=lifetimeVariable=lifetime

–Experimental unit = bulbExperimental unit = bulb

–Typical measurements: Typical measurements: 1503.1 hrs, 1010.5 hrs1503.1 hrs, 1010.5 hrs

ExamplesExamples

• Opinion pollsOpinion polls

–Variable = opinionVariable = opinion

–Experimental unit = personExperimental unit = person

–Typical Measurements = Typical Measurements = Magic Johnson, someone elseMagic Johnson, someone else

• Hair color Hair color

– Variable = Hair colorVariable = Hair color

– Experimental unit = PersonExperimental unit = Person

– Typical Measurements = Typical Measurements = Brown, black, blondeBrown, black, blonde

ExamplesExamples

Descriptive StatisticsDescriptive Statistics• When we can enumerate whole

population,

We use

• DESCRIPTIVE STATISTICS:DESCRIPTIVE STATISTICS: Procedures used to summarize and describe the set of measurements.

Inferential StatisticsInferential Statistics• When we cannot enumerate the whole

population, we use

• INFERENTIAL STATISTICS:INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample.

Objective of Objective of Inferential StatisticsInferential Statistics

• To make inferences about a population from information contained in a sample.

• The statistician’s job is to find the best way to do this.

But, our conclusions could be incorrect…But, our conclusions could be incorrect…consider this internet opinion poll…consider this internet opinion poll…

• Internet users only• Measure of reliability

We’ll PAY CASH For Your Opinions!(as much as $50,000 ) Click Here and sign up

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Who makes the best burgers? Votes Percent

McDonalds 123 Votes 13%

Burger King 384 Votes 39%

Wendy’s 304 Votes 31%

All three have equally good burgers 72 Votes 7%

None of these have good burgers 98 Votes 10%

The Steps in Inferential The Steps in Inferential StatisticsStatistics

• Define the objective of the experiment and the population of interest

• Determine the design of the experiment and the sampling plan to be used

• Collect and analyze the data• Make inferences about the population from

information in the sample• Determine the goodness or reliability of the

inference.

Key WordsKey Words

Experimental UnitExperimental Unit

PopulationPopulation

SampleSample

Descriptive StatisticsDescriptive Statistics

Inferential StatisticsInferential Statistics