Question

The number of degrees of freedom associated with a sample of size n is:

• A. One
• B. Infinite
• C. Zero
• D. Two

Hint:

Degrees of freedom:
- For a sample of size n: df = n-1.
- The number of constraints is 1 (the mean).
- Used in t-tests and ANOVA.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Degrees of freedom represent the number of independent values that are free to vary while estimating a statistical parameter, such as the sample mean.

Step 2: Key Formula or Approach:
For a sample containing \(n\) observations, the degrees of freedom are given by:
\[ \text{Degrees of Freedom} = n - 1 \] One degree of freedom is lost because the sample mean is calculated from the same data, creating one constraint.

Step 3: Detailed Explanation:
When the sample mean is known, the sum of deviations from the mean must always equal zero.
Therefore, after choosing values for \(n-1\) observations freely, the final observation is automatically determined.
This is why only one constraint exists in the sample, and the degrees of freedom become \(n-1\).
According to the given options, this corresponds to one degree being constrained.
Final Answer:
Therefore, the correct answer is (A) One.