Question

For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.

a. To the right of 2.120. (Use 3 decimals.) _______

b. To the left of 1.337. (Use 2 decimals.) __________

c. To the left of -1.746. (Use 2 decimals.) __________

d. To the right of 2.583. (Use 2 decimals.) ___________

e. Between -2.120 and 2.120. (Use 2 decimals.) __________

f. Between -1.746 and 1.746. (Use 2 decimals.)___________

Answer 1

Solution: Solution to this question requires t- table.

a) To the right of 2.120

As we know DoF = 16, T value = 2.120, and have to choose the right tail.

p = 0.025

b.) To the left of 1.337

DoF = 16 , T value = 1.337, and have to choose the left tail.

P = (1-0.1) = 0.90

c) To the left of -1.746.

DoF= 16, T value = -1.746 and have to choose the left tail

p = (1-0.95) = 0.05

d) To the right of 2.583. (Use 2 decimals.)

DoF= 16, T value = 2.583 and have to choose the right tail

p = 0.01

e) Between -2.120 and 2.120. (Use 2 decimals.)

P(T<-2.12) = 0.025

P(T<2.12) = 0.975

P(-2.12<T<2.12) = 0.975-0.025 = 0.95

f) Between -1.746 and 1.746. (Use 2 decimals.)

P(T<-1.746 ) = 0.05

P(T<1.746 ) = 0.95

P(-1.746 <T<1.746 ) = 0.95 - 0.05 = 0.90