Determine the t critical value (s) that will capture the desired t-curve area in each of the following cases. (Assume that central areas are centered at t = 0. Round your answers to three decimal places.)

a. Central area = 0.95, df = 10

b. Central area = 0.95, df = 20

c. Central area = 0.99, df = 20

d. Central area = 0.99, df = 60

e. Upper-tail area = 0.01, df = 30

f. Lower-tail area = 0.025, df = 5

Step-by-step explanation:

a) this involves 2 tails

The critical value is determined from the t distribution table.

α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Looking at 0.975 with df 10

The critical value is 2.228

b) α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Looking at 0.975 with df 20

The critical value is 2.086

c) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Looking at 0.995 with df 20

The critical value is 2.845

d) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Looking at 0.995 with df 60

The critical value is 2.660

e) 1 - α = 1 - 0.01 = 0.99

Looking at 0.99 with df 10

The critical value is 2.764

f) 1 - α = 1 - 0.025 = 0.975

Looking at 0.975 with df 5

The critical value is 2.571