Question

Chose the correct answer :

• 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:

Use a simple matrix to remember hypothesis testing outcomes:
- Reject a TRUE \(H_0\) \(\implies\) Type-I error (\(\alpha\)).
- Accept (Fail to Reject) a FALSE \(H_0\) \(\implies\) Type-II error (\(\beta\)).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In hypothesis testing, we make decisions about a population parameter based on sample data.
Since our decisions are based on sample statistics, there is always a possibility of making an incorrect decision.
We classify these incorrect decisions into two types of errors: Type-I error and Type-II error.

Step 2: Detailed Explanation:
Let us analyze the framework of decisions in statistical hypothesis testing.
The null hypothesis is denoted by \(H_0\) and the alternative hypothesis is denoted by \(H_1\).
A Type-I error occurs when we reject the null hypothesis \(H_0\) when it is actually true.
This is also known as a false positive, and its probability is denoted by the significance level \(\alpha\).
A Type-II error occurs when we fail to reject the null hypothesis \(H_0\) when it is actually false.
This is also known as a false negative, and its probability is denoted by \(\beta\).
Let us evaluate the options based on these definitions:
Option (A) states "Reject \(H_0\) when it is false is Type-I error", which is incorrect because rejecting a false null hypothesis is a correct decision.
Option (B) states "Reject \(H_0\) when it is true is Type-II error", which is incorrect because this is the definition of a Type-I error.
Option (C) states "Reject \(H_0\) when it is false is Type-II error", which is incorrect because failing to reject a false null hypothesis is a Type-II error.
Option (D) states "Reject \(H_0\) when it is true is Type-I error", which perfectly matches the definition of a Type-I error.

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