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Stat 281: Introduction to Probability and Statistics

Stat 281: Introduction to Probability and Statistics. A prisoner had just been sentenced for a heinous crime and was returned to his cell. An inquisitive guard could not wait to ask him about the outcome. Guard: “What did you get for a sentence?” Prisoner: “I could choose life or 100 years.”

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Stat 281: Introduction to Probability and Statistics

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  1. Stat 281: Introduction to Probability and Statistics A prisoner had just been sentenced for a heinous crime and was returned to his cell. An inquisitive guard could not wait to ask him about the outcome. Guard: “What did you get for a sentence?” Prisoner: “I could choose life or 100 years.” Guard: “And what did you choose?” Prisoner: “Well, life, obviously. Statistically speaking, that is the shorter sentence.”

  2. Hmmm… • A statistician is a mathematician broken down by age and sex. • Did you hear the one about the statistician? Probably…. • Statistics means never having to say you’re certain (or wrong).

  3. Seriously, though… • Definitions are crucial in stats class. If you don’t know the precise meaning of a word, the whole point of the sentence/paragraph/chapter could be lost! • Concepts are important in stats class. • Lots of formulas—don’t plug in numbers blindly—understand why • Review and integrate

  4. Definitions • Data (is/are?) • Population (of? Not a number) Finite/Infinite/Practically Infinite • Sample (proper subset, finite) • Variable (response, random) • Parameter/Statistic Greek/Latin • Experiment/Observational Study

  5. Probability vs. Statistics • Probability: Properties of population are known. Make predictions about sample. • Statistics: Sample is known. Guess (estimate) properties of population. • Statistics (is/are?) • Descriptive • Inferential

  6. Types of Data (Variables) • Categorical (Class, Attribute, Qualitative) • Numeric (Quantitative) • Discrete (Finite or Infinite) • Note: Finite/Infinite values, not populations • Continuous (always Infinite) • Measurement Scales • Nominal • Ordinal • Interval • Ratio

  7. Identify the Data Types 1. The daily high temperature (°F) in Brookings. 2. The make of automobile driven by each student. 3. The defect status of 9 volt batteries being tested. 4. The weight of a lead pencil. 5. The length of time billed for a long distance call. 6. Which brand of cereal children eat for breakfast. 7. The genre of a book checked out of the library. 8. The time until a pain reliever begins to work.

  8. Variation • No matter what the response variable: there will always be variability in the data. • One of the primary objectives of statistics: measuring and characterizing variability. • Controlling (or reducing) variability in a manufacturing process: statistical process control.

  9. Sampling Methods • Sampling Frame • Representative • Biased and Unbiased • Sampling Methods • Convenience • Volunteer • Judgment • Probability (“random”)

  10. Probability Sample Designs • Simple Random Sample • Systematic Sample • Stratified • Proportional (Quota) • Cluster

  11. The Role of Statistics • Central to science • Observation and experimentation must culminate with data • Hypotheses are evaluated based on results (data) • Correct conclusions are only possible if data are collected correctly and analyzed correctly • Central to many business, industry, and government activities. • Anybody who has to make objective decisions needs statistics. • Statistical thinking trains us to distinguish coincidences from meaningful patterns

  12. Are you above average? • The vast majority of people have more than the average number of legs. • “When she told me I was average, she was just being mean.” • You know how dumb the average person is? Well, half the population is dumber than that!

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