1. Chapter 20: Testing Hypotheses about Proportions
“Half the money I spend on advertising is wasted; the trouble is I don’t know which half.”
-John Wanamaker

2. Hypotheses Hypothesis:
a supposition
a proposition or principle which is supposed or taken for granted, in order to draw a conclusion or inference for proof of the point in question
In statistical tests of hypotheses, we assume that a hypothesis is true.
If the data are consistent with the hypothesis, we retain the hypothesis
If the data are not consistent with the hypothesis, we reject the hypothesis

3. Testing Hypotheses The Null Hypothesis
The starting hypothesis
The null hypothesis specifies a population model parameter of interest and proposes a value for the parameter
Standard Deviation (not Standard Error)
We assume the null hypothesis to be true, so we have a value for the model parameter p.

4. The Reasoning of Hypothesis Testing
Hypotheses
The null hypothesis
Translate our question into a statement about model parameters
Write
The alternative hypothesis
Contains the values of the parameter we accept if we reject the null.

5. The Reasoning of Hypothesis Testing
Plan
Specify the model you will use to test the null hypothesis and the parameter of interest
All models require assumptions, so state them and check any corresponding conditions
Include the name of the test you plan to perform
End with a statement such as
“Because the conditions are satisfied, it id appropriate
to model the sampling distribution of the proportion with a
model”

6. The Reasoning of Hypothesis Testing
Mechanics
Do the actual calculations of a test statistic from the data
The ultimate goal is to obtain a P-value
The probability that the observed statistic value could occur if the null model were correct
If the P-value is small enough, reject the null hypothesis

7. The Reasoning of Hypothesis Testing
Conclusion
The conclusion in a hypothesis test is always a statement about the null hypothesis
“reject” or “fail to reject” the null hypothesis
Consider the size of the effect by examining a confidence interval

8. One-proportion z-test
The conditions for the one-proportion z-test are the same as for the one-proportion z-interval.
When the conditions are met and the null hypothesis is true, the statistic follows the standard Normal model, so we can use that model to obtain a P-value.

9. Alternative Alternatives
Two-sided alternative
When we are equally interested in proportions that deviate from p in either direction

10. Alternative Alternatives
One-sided alternative
An alternative hypothesis that focuses on deviations from the null hypothesis value in only one direction.
The P-value is the probability of deviating only in the direction of the alternative away from the null hypothesis value

11. TI-83+ Tips
STAT TESTS
5: 1-Prop ZTest

12. TI-83+ Tips Specify the hypothesized proportion Po
Enter x, the observed number of wins
Specify the sample size
Decide on one- or two-tailed test
Calculate

13. P-Values and Decisions: What to Tell About a Hypothesis Test
Hypothesis tests are useful when making a decision
It is a good idea to report the confidence interval for the parameter of interest
The P-value is highly context-dependent
The importance of the issue also factors into the choice of P-value
The conclusion about any null hypothesis should be accompanied by the P-value of the test. If possible, it should also include a confidence interval for the parameter of interest