Stat 281: Introduction to Probability and Statistics

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 youre
  certain (or wrong).

3
Seriously, though

• Definitions are crucial in stats class.
• If you dont 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 formulasdont plug in numbers
  blindlyunderstand 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

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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

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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

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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!