gen-define-type-i-and-type-ii-errors-and-give-one-short-worked-e-f1ba

Define type I and type II errors and give one short worked example.

# Type I and Type II Errors ## Definitions **Type I Error (α)**: Rejecting the null hypothesis when it is actually **true** - Also called a "false positive" - The significance level (α) is the probability of making this error **Type II Error (β)**: Failing to reject the null hypothesis when it is actually **false** - Also called a "false negative" - Power = 1 - β is the probability of correctly rejecting a false null hypothesis ## Worked Example **Scenario**: A pharmaceutical company tests whether a new drug reduces blood pressure. - **H₀** (null hypothesis): The drug has no effect - **H₁** (alternative hypothesis): The drug reduces blood pressure **Type I Error**: The company concludes the drug works (rejects H₀) when it actually doesn't. They may market an ineffective drug. **Type II Error**: The company concludes the drug doesn't work (fails to reject H₀) when it actually does. They may abandon an effective treatment. --- ### Summary Table | | **H₀ is True** | **H₀ is False** | |--------------------------|--------------------|--------------------| | **Reject H₀** | Type I Error (α) | Correct decision ✓ | | **Fail to reject H₀** | Correct decision ✓ | Type II Error (β) |