Question

1a For the following degrees of freedom, list the critical values for a two-tailed test at a .01, .05, and .10 level of significance.

                                        .01           .05           .10  

                        df = 8               ___          ___          ___

                        df = 20             ___          ___          ___

                        df = 40             ___          ___          ___

                        df = 120   ___          ___          ___

b. As the level of significance increases (from .01 to .10), does the critical value increase or decrease?

c. As the degrees of freedom increase (from 8 to 120), does the critical value increase or decrease?

d. How is this related to power? Hint: If you are having trouble, refer to Sections 8.8 and 8.9 in Chapter 8 for a review of factors that influence power.

Answer 1

a)   We use the Excel function T.INV.2t to find the t-critical values
= T.INV.2T(level of significance, deg_freedom)

	0.01	0.05	0.1
df = 8	3.355	2.306	1.860
df = 20	2.845	2.086	1.725
df = 40	2.704	2.021	1.684
df = 120	2.617	1.980	1.658

b)   As the level of significance increases, we can see that the
critical value decreases
  
c)   As the degrees of freedom increase, we can see that the
critical value decreases
  
d)   Using a higher significance level increases the probability that you reject the null hypothesis.
Thus probability of committing a Type II error decreases (Type II error : Accept Ho when it is not true)
Power = 1 - P(Type II error)
Hence, as the significance level increases, the power of the test increases
  
Test with small degrees of freedom will attain higher power than the same test with larger degrees of freedom
As the degrees of freedom increase, the power of the test decreases