1. The Language of Statistical Decision Making
Lecture 1
Section 1.3
Fri, Jan 16, 2004

2. Populations and Samples
Population – The entire group of objects or individuals under study.
Sample – A part of the population that is actually used to get information.

3. Populations and Samples
The population is the group of individuals that we wish to learn something about.
The trouble is, it is too big to study directly.
The sample is small enough to study.
Hopefully, the sample will be representative of the population.

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

5. Statistical Inferences
We generally assume that our sample is representative of the population, within certain limits (to be calculated later).
This allows us to conclude that what we observe to be true in the sample should be close to what is true in the population.

6. Statistical Inferences
Keep in mind:
What we observe in the sample is known to be true.
What we infer about the population is not known to be true.

7. Hypotheses
Hypothesis – A statement that is proposed, but not known to be true.
Hypotheses are often explanations of something that is known to be true.
There are many hypotheses about what happened to the European Union’s Mars lander on Christmas day.
No one really knows what happened.

8. Hypotheses
In statistics, we start with two hypotheses about a population.
The Null Hypothesis – The conventional belief.
The Alternative Hypothesis – An alternative to the null hypothesis.
See Example 1.1, p. 4.

9. Hypotheses The null hypothesis gets the benefit of the doubt.
The alternative hypothesis bears the burden of proof.

10. Hypotheses The evidence is either
Clearly in favor of the null hypothesis, or
Clearly in favor of the alternative hypothesis, or
Not clearly in favor of either hypothesis.
When the evidence is not clear, we give the benefit of the doubt to the null hypothesis.

11. The Decision
We will decide either to accept or to reject the null hypothesis.
We will accept the null hypothesis if the evidence is either
Clearly in favor of the null hypothesis, or
Not clearly in favor of either hypothesis.

12. The Decision We will reject the null hypothesis if the evidence is
Clearly in favor of the alternative hypothesis.

13. Let’s Do It! Let’s do it! 1.1 – Fair Die?
Let’s do it! 1.2 – Stress Can Cause Sneezes.

14. Example 1.2
See Example 1.2, p. 7.
If 1/5 of the balls are yellow, then
The likelihood of drawing five yellow balls in a row is 0.032%.
The likelihood of drawing five blue balls in a row is 32.8%.

15. Example 1.2 Scenario 1: Suppose we draw 5 yellow balls in a row.
Is the evidence clearly in favor of one hypothesis?
Scenario 2: Suppose we draw 5 blue balls in a row.

16. Example 1.2
Notice that H1 does not specify the proportion of yellow balls, except to say that it is greater than 1/5.
Therefore, we cannot calculate the likelihood of drawing 5 yellow balls or 5 blue balls when H1 is true.