Minimum degree of freedom required to draw the valid results is:

Correct option is C

Understanding Degrees of Freedom (df):
In statistics, degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution.
It is a crucial component in various hypothesis testing methods such as:
t-test
Chi-square test
ANOVA (Analysis of Variance)
�� Why a Minimum of 12 Degrees of Freedom?
For many statistical tests, especially Chi-square tests, it is recommended to have a minimum degrees of freedom to ensure the test results are statistically valid and accurate.
Generally, as the degrees of freedom increase, the test results become more reliable, because:
The sample size is larger.
The approximations to the distribution (e.g., normal or chi-square) are better.
A commonly accepted rule of thumb is that a minimum of 12 degrees of freedom ensures a sufficiently accurate approximation, especially when using the Chi-square test.
�� Chi-square tests require that:
Expected frequency in each category should be ≥ 5.
The total degrees of freedom should be ≥ 12 to avoid errors in significance interpretation.
�� Other Options Explained:
(a) 8, (b) 10, and (d) 14 are values that may be used in practice, but 12 is often the critical threshold for valid statistical inference in standard tables and analysis.
✅ Correct Answer:
(c) 12
Let me know if you want examples where this threshold is applied (e.g., Chi-square test on categorical data).