Question

The minimum number of blocks required for 6 treatments so that the error degrees of freedom is 10 in case of a randomized complete block design is:

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

Exam Tip:
In RCBD:

• Total df = \(bt - 1\).
• Block df = \(b - 1\).
• Treatment df = \(t - 1\).
• Error df = \((t - 1)(b - 1)\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In a randomized complete block design (RCBD) with \(t\) treatments and \(b\) blocks, the degrees of freedom for error are: \[ \text{df}_{\text{error}} = (t - 1)(b - 1) \]

Step 2: Key Formula or Approach:
We have \(t = 6\) and we need \(\text{df}_{\text{error}} = 10\).
So, \[ (6 - 1)(b - 1) = 10 \Rightarrow 5(b - 1) = 10 \Rightarrow b - 1 = 2 \Rightarrow b = 3 \]

Step 3: Detailed Explanation:
With \(t = 6\), the minimum number of blocks \(b\) needed to get 10 error degrees of freedom is 3.
Check: \((6 - 1)(3 - 1) = 5 \times 2 = 10\).
So, 3 blocks are sufficient.

Step 4: Final Answer:
Therefore, option (B) is correct.