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Introduction to Probability and Statistics Fourteenth Edition Introduction Train Your Brain for Statistics

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What is Statistics? What does a statistician do? Player Games Minutes Points Rebounds FG% Bob 34 32.724 7.6.552 Andy 36 31.521 8.4.465 Larry 30 33.018 5.6.493 Michael 31 35.129 6.1.422 Player Games Minutes Points Rebounds FG% Bob 34 32.724 7.6.552 Andy 36 31.521 8.4.465 Larry 30 33.018 5.6.493 Michael 31 35.129 6.1.422

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Job of a Statistician Collects numbers or data Organizes or arranges the data Analyzes the data Infers general conclusions

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Uses 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

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POLITICS 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, who would you be more likely to vote for? James Hahn32% Magic Johnson36% Someone else11% No opinion yet21% If the election for mayor of Los Angeles were held today, who would you be more likely to vote for? James Hahn32% Magic Johnson36% Someone else11% No opinion yet21%

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To market product Average length of life of a light bulb? What should statistician do? (cannot test all the bulbs) INDUSTRY

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Solution Collect a smaller set of measurements that will (hopefully) be representative of the whole set. POPULATION:POPULATION: set of all measurements SAMPLE:SAMPLE: A subset of population

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Definitions Variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration Experimental Units are items or objects on which measurements are taken Measurement results when a variable is actually measured on an experimental unit Population is the WHOLE set of all possible measurements Sample is a subset of population

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Examples Light bulbsLight bulbs –Variable=lifetime –Experimental unit = bulb –Typical measurements: 1503.1 hrs, 1010.5 hrs

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Examples Opinion pollsOpinion polls –Variable = opinion –Experimental unit = person –Typical Measurements = Magic Johnson, someone else

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Hair colorHair color –Variable = Hair color –Experimental unit = Person –Typical Measurements = Brown, black, blonde Examples

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Descriptive Statistics When we can enumerate whole population, We use DESCRIPTIVE STATISTICS:DESCRIPTIVE STATISTICS: Procedures used to summarize and describe the set of measurements.

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Inferential 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.

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Objective of Inferential 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.

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But, our conclusions could be incorrect…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 FREE! Who makes the best burgers?VotesPercent McDonalds123 Votes13% Burger King384 Votes39% Wendy’s304 Votes31% All three have equally good burgers72 Votes7% None of these have good burgers98 Votes10%

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The Steps in Inferential Statistics 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.

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Key Words Experimental Unit PopulationSample Descriptive Statistics Inferential Statistics

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