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.
One-tailed test, α = .05, n = 10
Two-tailed test, α = .05, n = 10
One-tailed test, α = .01, n = 15
Two-tailed test, α = .01, n = 20
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
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