Question

If the null hypothesis \(H_0\) is rejected when it is actually true, what type of error has been committed?

• A. Type I Error
• B. Type II Error
• C. Sampling Error
• D. Standard Error

Hint:

Remember the two main hypothesis testing errors: \[ \text{Type I Error: Reject } H_0 \text{ when it is true} \] \[ \text{Type II Error: Fail to reject } H_0 \text{ when it is false} \] Type I error probability is the \textbf{significance level} \( \alpha \).

Answer 1

The Correct Option is A

Step 1: Understanding the Question 
The question describes a scenario in hypothesis testing where a decision is made to reject the null hypothesis (\(H_0\)), but in reality, the null hypothesis was true. We need to identify the name for this specific type of mistake. 
Step 2: Detailed Explanation
In hypothesis testing, there are four possible outcomes based on our decision and the true state of nature: 


Type I Error: Rejecting a true null hypothesis. The probability of this error is denoted by \(\alpha\), the significance level. 

Type II Error: Failing to reject a false null hypothesis. The probability of this error is denoted by \(\beta\). 

The scenario described—rejecting \(H_0\) when it is actually true—is the exact definition of a Type I Error. 
Step 3: Final Answer
The error committed is a Type I Error.