1. Unit 9: Testing a Claim
9.1C—Type I/Type II Errors and the Power of a Test
9.2A—Significance Test for a Population Proportion

2. Objectives 9.1C:
Describe and interpret Type I and Type II errors in context
Describe how to change the Power of a test

3. True state of the universe Decision we make based on the sample
Ho is True
Ho is False
Decision we make based on the sample
Reject Ho
Type I error
Correct Decision
Fail to reject Ho
Type II error

4. The academy of motion pictures wants to assess the preferences of its customer base. If the majority of Americans prefer to watch their movies at home, then more money will need to be spent on marketing to the home viewer. The relevant hypotheses are:
𝐻 𝑜 :𝑝=0.50
𝐻 𝑎 :𝑝>0.50
Describe a Type I error in the context of this problem.
Describe the consequences of a Type II error.

5. True state of the universe Decision we make based on the sample
Ho is True
Ho is False
Decision we make based on the sample
Reject Ho
Type I error
Correct Decision
Fail to reject Ho
Type II error
P(Type I error) = α
P(Type II error) = β
But α is also the significance level….and we choose that ourselves!

6. The power of a statistical test is the probability that the test will reject the null hypothesis when the null hypothesis is false (i.e. the probability of not committing a Type II error)
Power = 1 − β

7. How do you get higher power?
Increase your sample size
Increase α
Collect data in a way that reduces variability (stratification, blocking)
Move the hypothesized value farther from the true value of the parameter….

8. Objectives 9.2A:
Perform a significance test
Write hypotheses
Check conditions
Perform the mechanics
Make a decision linked in context

9. Conditions:
Random
Independent
Normal
(What a shock!)

10. Example:
Is it better to go last?
600 fans of an American Idol type show were shown the audition tapes of 12 people in random order. 59 choose the last tape as their favorite. Does this sample provide support for the claim that it is advantageous to go last?

11. Are young people at risk for heart disease?
Example:
Are young people at risk for heart disease?
In 2005, researchers studies the physical fitness of adolescents aged 12 to 19 years. Of the 2205 tests, 750 showed a poor level of cardiovascular fitness. Does this sample provide support for the claim that more than 30% of adolescents have a low level of cardiovascular fitness?

12. Example:
Fewer Parolees Land Back in Prison
Quote: “Just over 38% of all felons who were released from prison in 2003 landed back in jail by the end of the following year.”
Explain why it would not be necessary to carry out a hypothesis test to see if the proportion of felons released in 2003 was less than 40%.