Hypothesis Testing
Chapter 12
(Part 1)
Example
Suppose Jill Thrillseeker is going sky diving. Jill will be inspecting the parachute before using it. No matter the inspection, we can never be 100% sure the parachute will work until we pull the rip cord to deploy it.
\(H_0:\) the parachute is packed correctly (meaning it will work)
\(H_A:\) the parachute is not packed correctly (meaning it will not work)
Describe the 4 possible scenarios and their consequences.
| Alternative \(H_A\) is true | Null \(H_0\) is true | |
|---|---|---|
| Reject the null hypothesis | Scenario 1 | Scenario 2 |
| Do not reject the null hypothesis | Scenario 3 | Scenario 4 |
4 Possible Scenarios Results
| Alternative \(H_A\) is true | Null \(H_0\) is true | |
|---|---|---|
| Reject the null hypothesis | Correct Decision | Type I Error |
| Do not reject the null hypothesis | Type II Error | Correct Decision |
Error
- Reject the null hypothesis when it is true
- False Positive
- Significance level
- \(\alpha\) = probability of a Type I error
- Fail to reject the null hypothesis when it is false
- False Negative
- \(\beta\) = probability of a Type II error
- The probability of correctly rejecting the null hypothesis when it is false
- Correct rejection decision
- \(\textbf{Power} = 1 - \beta\)
