Question

As the degrees of freedom increase (from 20 to 120), does the critical value increase or decrease? Would that make the region of rejection larger or smaller?

Answer 1

As the degrees of freedom increase (from 20 to 120), does the critical value increase or decrease?

If we increased the degree of freedom from 20 to 120, then critical value will be decreased.

because degree of freedom(df) = N - 1 [ N means sample size]. (in t test)

small sample size critical value will be high when compared to large sample size. Because in small sample size variability of scores will be high so it requires large critical value to reject null hypothesis. But in large sample size variability of scores will be less.So it requires less critical value to reject null hypothesis.

Example:(refer t table)

Critical value for degree of freedom 20 (df=20) is 1.725 ( in one tailed t test)

Critical value for degree of freedom 120 (df=120) is 1.655 (in one tailed t test).

This example proving that critical value will be decreased if we increase degree of freedom from 20 to 120

Would that make the region of rejection larger or smaller?

This makes region of rejection larger.Because critical value and region of rejection are in inversly proportional.If one parameter increased,then other parameter will be decreased.

In given case critical value decreased so region of rejection will be increased.In otherwords region of rejection will became larger.