In reference to Inferential Statistics, for 20 degrees of freedom, the least statistical t-value among the given below is:

The question asks for the smallest t-value among the given options for 20 degrees of freedom.

The numbers in brackets (0.005, 0.01, 0.025, 0.05) represent significance levels or tail probabilities (α).

The relationship between significance level and t-value follows this principle:

Larger α (significance level) corresponds to smaller t-value

Smaller α (significance level) corresponds to larger t-value

Comparing the given significance levels:

α = 0.005 (smallest α, largest t-value)

α = 0.01 (small α, large t-value)

α = 0.025 (medium α, medium t-value)

α = 0.05 (largest α, smallest t-value)

Since 0.05 is the largest significance level among the options, $t_{(0.05)}$ gives the smallest t-value.

A larger tail probability (0.05 or 5%) represents a less extreme cutoff point on the t-distribution, requiring a smaller t-value. A smaller tail probability (0.005 or 0.5%) represents a more extreme cutoff point, requiring a larger t-value.

The least statistical t-value is $t_{(0.05)}$