Question

19. Using the t distribution table, identify the t statistics that would set the critical regions in a hypothesis test for the following alphas and n’s (2 points each). Remember to check direction and df when choosing the column/row.  

1. One-tailed test, α = .05, n = 10

2. Two-tailed test, α = .05, n = 10

3. One-tailed test, α = .01, n = 15

4. Two-tailed test, α = .01, n = 20

Answer 1

Solution:

a)

df = n - 1 = 10 - 1 = 9

For one tailed test , critical value is = t_0.05,9 = 1.833

If left tailed , the critical region is < -1.833

If right tailed , the critical region is > 1.833

b)

Two tailed test

α = .05

α/2 = 0.025

Critical value are

t_0.025,9 = 2.262

Critical values are -2.262 , 2.262

Critical regions are : < -2.262 or > 2.262

c)

df = n - 1 = 15 - 1 = 14

For one tailed test , critical value is = t_0.01,14 = 2.624

If left tailed , the critical region is < -2.624

If right tailed , the critical region is > 2.624

d)

df = n - 1 = 20 - 1 = 19

Two tailed test

α = .01

α/2 = 0.005

Critical value are

t_0.005,19 = 2.861

Critical values are -2.861, 2.861

Critical regions are : < -2.861 or > 2.861