Question

Chose the correct answer :
(1) Reject \(H_0\) when it is false is Type-I error
(2) Reject \(H_0\) when it is true is Type-II error
(3) Reject \(H_0\) when it is false is Type-II error
(4) Reject \(H_0\) when it is true is Type-I error

• A. Reject \(H_0\) when it is false is Type-I error
• B. Reject \(H_0\) when it is true is Type-II error
• C. Reject \(H_0\) when it is false is Type-II error
• D. Reject \(H_0\) when it is true is Type-I error

Hint:

Remember this simple matrix to avoid confusion:
- Reject \(H_0\) when \(H_0\) is True \(\implies\) Type-I Error (\(\alpha\)).
- Accept \(H_0\) when \(H_0\) is False \(\implies\) Type-II Error (\(\beta\)).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In statistical hypothesis testing, we make decisions about a population parameter based on sample data.
Because we rely on samples, there is always a probability of making incorrect decisions.
These errors are classified into two categories: Type-I error (\(\alpha\)) and Type-II error (\(\beta\)).

Step 2: Detailed Explanation:
Let us systematically define the errors associated with testing a null hypothesis (\(H_0\)):
1. Type-I Error (\(\alpha\)): This error occurs when we reject the null hypothesis (\(H_0\)) when it is actually true.
It is often called a "false positive" because we conclude that an effect exists when it actually does not.
The probability of committing a Type-I error is denoted by \(\alpha\), which is also the significance level of the test.
2. Type-II Error (\(\beta\)): This error occurs when we fail to reject (accept) the null hypothesis (\(H_0\)) when it is actually false.
It is often called a "false negative" because we miss an effect that actually exists.
The probability of committing a Type-II error is denoted by \(\beta\), and \(1-\beta\) is defined as the power of the test.
Let us evaluate the options:
- Option (A) is incorrect because rejecting a false null hypothesis is a correct decision (power of the test).
- Option (B) is incorrect because rejecting a true null hypothesis is a Type-I error, not Type-II.
- Option (C) is incorrect because accepting a false null hypothesis is a Type-II error, not rejecting it.
- Option (D) correctly defines Type-I error as the rejection of a true null hypothesis (\(H_0\)).
Thus, Option (D) is the correct statement.

Step 3: Final Answer:
The correct option is (D).