1. The Language of Statistical Decision Making
Lecture 1
Section 1.3
Fri, Sep 2, 2005

2. Populations and Samples
Population – The entire group of objects or individuals under study.
Sample – A part of the population from which the data is actually obtained.

3. Statistical Inferences
Statistical inference – A conclusion about the population based on information from a sample of that population.

4. Samples and Inferences
Population

5. Samples and Inferences
Population
Take
Sample
Sample

6. Samples and Inferences
Population
Take
Sample
Make Observations
Sample
Data

7. Samples and Inferences
Population
Inference
Draw an
Inference
Take
Sample
Make Observations
Sample
Data

8. Samples and Inferences
Population
Inference
Draw an
Inference
Take
Sample
Make Observations
Sample
Data

9. Hypotheses
Hypothesis – A statement that is proposed, but not known to be true.
Hypotheses are often proposed explanations of something that is known to be true.

10. Hypotheses
The Null Hypothesis – The conventional belief about the population, or the status quo.
It receives the benefit of the doubt.
The Alternative (Research) Hypothesis – An alternative to the null hypothesis.
It bears the burden of proof.
Typically, the researchers are trying to prove the alternative hypothesis.

11. Hypothesis Testing
Population

12. Hypothesis Testing
Null
Hypothesis
Population

13. Hypothesis Testing
Null
Hypothesis
Population
Alternative
Hypothesis

14. Hypothesis Testing Null Hypothesis Population Alternative Hypothesis
Sample

15. Hypothesis Testing Null Hypothesis Population Alternative Hypothesis
Sample
Evidence

16. Hypothesis Testing Null Hypothesis Population Alternative Hypothesis
Which
Hypothesis Is
Supported?
Sample
Evidence

17. Hypothesis Testing Null Hypothesis Population The evidence may support
the Null
Hypothesis…
Sample
Evidence

18. Hypothesis Testing Null Hypothesis Population …if any discrepancy
can be
attributed
to chance
Sample
Evidence

19. Hypothesis Testing Population Alternative Hypothesis The evidence will
support the
Alternative
Hypothesis…
Sample
Evidence

20. Hypothesis Testing Population Alternative Hypothesis …if the
discrepancy
cannot be
attributed
to chance
Sample
Evidence

21. Statistical Significance
The data are called statistically significant if their deviation from what would be expected under the null hypothesis is too great to be attributed to chance.
Example: The incidence of cancer in one community is 8% and in another community it is 10%. Can the difference be attributed to chance?

22. Let’s Do It! Let’s do it! 1.1, p. 6 – Fair Die?
Let’s do it! 1.2, p. 7 – Stress Can Cause Sneezes.
Example 1.3, p. 9 – Is the New Drug Better?
What are the risks involved in making the wrong decision?
See Making Intelligent Errors, by Walter Williams.