What is Type 1 and Type 2 errors in Null Hypothesis

**Example of a Type 1 Error:**

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### **Scenario: Medical Testing for a Disease**

- **Null Hypothesis (\(H_0\))**: The patient does **not** have the disease.

- **Alternative Hypothesis (\(H_a\))**: The patient **has** the disease.

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### **What Happens in a Type 1 Error:**

1. **Reality**: The patient is actually **healthy** (null hypothesis is **true**).

2. **Test Result**: The diagnostic test incorrectly shows **positive** for the disease.

3. **Decision**: Doctor rejects the null hypothesis and concludes the patient **has** the disease.

4. **Outcome**: **False positive** – the patient is told they have a disease they don't actually have.

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### **Consequences:**

- Unnecessary stress and anxiety for the patient

- Further invasive testing that wasn't needed

- Wasted medical resources

- Potential side effects from unnecessary treatment

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### **Statistical Context:**

- **Significance level (α)**: The probability of making a Type 1 error

- If α = 0.05, there's a 5% chance of rejecting a true null hypothesis

- In our example: 5% chance of diagnosing a healthy person as sick

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### **Other Real-World Examples:**

1. **Justice System**: Convicting an innocent person (null: defendant is innocent)

2. **Quality Control**: Rejecting a good batch of products (null: batch meets quality standards)

3. **Drug Testing**: Concluding a drug works when it doesn't (null: drug has no effect)

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**Type 1 errors represent "false alarms" – we see an effect that isn't really there.**