1. Section 11.4: Using Inference to Make Decisions
AP Statistics
Section 11.4: Using Inference to Make Decisions

2. Objective: To be able to calculate and understand Type I error, Type II error and Power.
Type I error: The probability that we reject 𝐻 0 when 𝐻 0 is true. 𝑃 𝑟𝑒𝑗𝑒𝑐𝑡 𝐻 0 𝐻 0 𝑖𝑠 𝑡𝑟𝑢𝑒)=𝛼
Type II error: The probability that we accept 𝐻 0 when 𝐻 𝑎 is true. 𝑃 𝑎𝑐𝑐𝑒𝑝𝑡 𝐻 0 𝐻 𝑎 𝑖𝑠 𝑡𝑟𝑢𝑒)=𝛽
Power: The probability that we reject 𝐻 0 when 𝐻 𝑎 is true. 𝑃 𝑟𝑒𝑗𝑒𝑐𝑡 𝐻 0 𝐻 𝑎 𝑖𝑠 𝑡𝑟𝑢𝑒)=1−𝛽

3. Points regarding Power:
Be sure you can interpret in the context of a problem.
The standard power level is 0.80.
Tests usual report power instead of type II error.
The higher the power the more sensitive the test is to specific alternatives.
Diagram: Truth about the Population
Decision
based on a
sample.
Ho is true
Ha is true
Reject Ho
Accept Ho

4. Ex 1. “Innocent until proven guilty.”
State the hypotheses in terms of the expression.
Interpret Type I and Type II errors in the context of the expression.
Type I error:
Type II error:
Which is more costly and why?

5. Ex 2. Draw two normal curves and label Type I error, Type II error and Power. Use 𝑯 𝒂 : 𝝁> 𝝁 𝟎 .

6. Ways to increase power: 1. 2. 3. 4
Ways to increase power: Method for calculating Type II error: 1. Write a rule for accepting Ho in terms of 𝑥 . 2. Find P(accept Ho | 𝜇= 𝜇 𝑎 ). 𝜇 𝑎 is a value that is provided to us in the region of Ha.

7. Ex 4. Calculate Type II error and power given the following scenario: 𝐻 0 :𝜇=8; 𝐻 𝑎 :𝜇<8; 𝜎=0.5; n=25; 𝜇 𝑎 =7.75