Question

Match List-I with List-II: 

List-I		List-II
(A)	Fail to reject the null hypothesis when it is true	(I)	Correct Decision
(B)	Fail to reject the null hypothesis when it is false	(II)	Type II Error (β Error)
(C)	Reject the null hypothesis when it is true	(III)	Type I Error (α Error)
(D)	Reject the null hypothesis when it is false	(IV)	Correct Decision (Power of Test)

• A. A-I, B-II, C-III, D-IV
• B. A-II, B-III, C-IV, D-I
• C. A-III, B-IV, C-I, D-II
• D. A-IV, B-I, C-II, D-III

Hint:

Rejecting a true null hypothesis is Type-I error. Failing to reject a false null hypothesis is Type-II error.

Answer 1

The Correct Option is B

Concept:
In hypothesis testing, decisions are classified as correct decisions or errors depending on the truth of the null hypothesis.

Step 1: Fail to reject \(H_0\) when \(H_0\) is true.
This is a correct decision. \[ A\rightarrow II \]

Step 2: Fail to reject \(H_0\) when \(H_0\) is false.
This is Type-II error. \[ B\rightarrow III \]

Step 3: Reject \(H_0\) when \(H_0\) is true.
This is Type-I error. \[ C\rightarrow IV \]

Step 4: Reject \(H_0\) when \(H_0\) is false.
This is a correct decision and is related to the power of the test. \[ D\rightarrow I \] Therefore: \[ A-II,\ B-III,\ C-IV,\ D-I \] \[ \therefore \text{Correct Answer is (B)} \]