Question

Find the critical value of t for each of the following:

Please show work and explain.

a. 1-α = 0.95, n=21

b. 1-α = 0.99, n=21

c. 1-α = 0.90, n=32

d. 1-α = 0.99, n=65

Answer 1

a. ) 1-α = 0.95, n=21

Solution :

1- = 0.95

   = 0.05

n=21

degree of freedom= n-1

d.f= 20

The t-critical values for a two-tailed test, for a significance level of α=0.05 are

t(n-1,/2)= -2.086 and t(n-1,/2)= 2.086 (by online calculate)

b) 1-α = 0.99, n=21

Solution :

1- = 0.99

   = 0.01

n=21

degree of freedom= n-1

d.f= 20

  The t-critical values for a two-tailed test, for a significance level of α=0.01 are

   t(n-1,/2) = t(20,0.005)

= −2.845 and 2.845 (by online calculate)

  

c ) 1-α = 0.90, n=32

Solution :

1- = 0.90

   = 0.1

n=32

degree of freedom= n-1

d.f= 31

  The t-critical values for a two-tailed test, for a significance level of α=0.1 are

t(n-1,/2) = t(31,0.05)

=  −1.696   and  1.696   (by online calculate)

  

  

d.) 1-α = 0.99, n=65

Solution :

1- = 0.99

   = 0.01

n=65

degree of freedom= n-1

d.f= 64

  The t-critical values for a two-tailed test, for a significance level of α=0.01 are

   t(n-1,/2) = t(64,0.005)

=  −2.655 and  2.655 (by online calculate)