Question

For a field experiment conducted in RBD with 4 replications and 6 treatments, compute standard error of mean, if error sum of squares is 120.

• A. 1.73
• B. 2.23
• C. 2.80
• D. 1.41

Hint:

SEM = \(\sqrt{\text{Error MS} / \text{r}}\).
Error MS = Error SS Error df.
Always check degrees of freedom.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Standard error of mean (SEM) measures the precision of the mean.
It is calculated from error mean square and replication number.

Step 2: Key Formula or Approach:
SEM = \(\sqrt{\text{Error Mean Square} / \text{Replications}}\).
Error Mean Square = Error Sum of Squares Error degrees of freedom.
Error degrees of freedom = (r - 1) \(\times\) (t - 1), where r = replications, t = treatments.

Step 3: Detailed Explanation:
Given: r = 4, t = 6, Error SS = 120.
Error df = (4 - 1) \(\times\) (6 - 1) = 3 \(\times\) 5 = 15.
Error Mean Square = 120 15 = 8.
SEM = \(\sqrt{8 / 4} = \sqrt{2} = 1.414\).
But 1.414 is not an option.
Wait, let's recheck:
SEM = \(\sqrt{\text{Error MS} / \text{r}} = \sqrt{8 / 4} = \sqrt{2} = 1.414\).
Option (D) is 1.41.
But the answer is given as (B) 2.
Maybe SEM = \(\sqrt{\text{Error MS}}\).
If we use SEM = \(\sqrt{\text{Error MS}} = \sqrt{8} = 2.828\).
Not matching.
If we use SEM = \(\sqrt{\text{Error MS} / \text{r}} = \sqrt{8/4} = 1.414\).
But the answer is 2.
Let's check: Error MS = 8.
SEM = \(\sqrt{8 / 4} = 1.414\).
Maybe SEM = \(\sqrt{(2 \times \text{Error MS}) / \text{r}}\).
SEM = \(\sqrt{(2 \times 8) / 4} = \sqrt{4} = 2\).
Not matching.
Perhaps the formula is SEM = \(\sqrt{\text{Error MS} / \text{r}}\).
1.414 is closest to 1.41.
But the answer given is (B) 2.
Let's reconsider: Error df = (r - 1)(t - 1) = (4-1)(6-1) = 15.
Error MS = 120/15 = 8.
SEM = \(\sqrt{8/4} = 1.414\).
The correct answer should be 1.41 (Option D).
I'll go with (D) 1.41.

Step 4: Final Answer:
The standard error of mean is 1.41.
Hence, the correct option is (D).