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### 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.”

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).

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

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

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

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

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.

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.

Sampling Methods

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

Probability Sample Designs

- Simple Random Sample
- Systematic Sample
- Stratified
- Proportional (Quota)
- Cluster

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

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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