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

2. What does a statistician do?
What is Statistics?
What does a statistician do?
Player Games Minutes Points Rebounds FG%
Bob
Andy
Larry
Michael

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

4. 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

5. POLITICS Forecasting and predicting winners Where to concentrate
If the election for mayor of Los Angeles were held today, who would you be more likely to vote for?
James Hahn 32%
Magic Johnson 36%
Someone else 11%
No opinion yet 21%
Forecasting and predicting winners
Where to concentrate
What should a statistician DO? (Cannot survey on every voter)

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

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

8. 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

9. Examples
Light bulbs
Variable=lifetime
Experimental unit = bulb
Typical measurements: hrs, hrs

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

11. Experimental unit = Person Typical Measurements = Brown, black, blonde
Examples
Hair color
Variable = Hair color
Experimental unit = Person
Typical Measurements = Brown, black, blonde

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

13. Inferential Statistics
When we cannot enumerate the whole population,
we use
INFERENTIAL STATISTICS: Procedures used to draw conclusions or inferences about the population from information contained in the sample.

14. 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.

15. But, our conclusions could be incorrect…consider this internet opinion poll…
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%
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Internet users only
Measure of reliability

16. 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.

17. Key Words
Variable Experimental Unit Population Sample Descriptive Statistics Inferential Statistics