Question

if we assume that the degree of freedom is fixed as an absolute value of the T-Stat gets bigger what happens to the corresponding P value

Answer 1

Solution:

T distribution has mean 0, so if degrees of remains fixed and if absolute T-stat value gets bigger then area in right tail decreases.

P-value is the area in tails corresponding to T-Stat value.

That is if T-stat = 2.123 then

P-value = P( T > 2.123) in case one tailed hypothesis.

Lets consider an example with df = 10 and assume this is two tailed test then we have:

From above table we can see, as T values increases or getting bigger , corresponding two tail area is decreasing, that means p-value is decreasing

thus as degree of freedom is fixed as an absolute value of the T-Stat gets bigger then corresponding P value decreases or gets smaller.