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

Concept:
In hypothesis testing, two types of errors may occur when making a decision about the null hypothesis.

• Type I Error: Rejecting the null hypothesis \(H_0\) when it is actually true.
• Type II Error: Failing to reject the null hypothesis \(H_0\) when it is actually false.

The probability of committing a Type I error is denoted by \( \alpha \), which is also called the level of significance.
Step 1: Understand the situation given in the question.
The question states that the null hypothesis \(H_0\) is rejected even though it is actually true.
Step 2: Identify the type of error.
This situation exactly matches the definition of a Type I Error.
Step 3: State the conclusion.
\[ \therefore \text{Rejecting a true null hypothesis results in a Type I Error.
\]