Question

State the total degrees of freedom for the following t-tests. (If you need to use ∞, enter INFINITY.)

(a)

n = 14

for a one-independent sample t-test


(b)

df₁ = 15, n₂ = 25

for a two-independent sample t-test


(c) critical value = 63.657 for a two-tailed test,

α = 0.01

(d) critical value = 1.645 for a one-tailed test,

α = 0.05

Answer 1

Solution:

We have to find  the total degrees of freedom for the following t-tests.

Part a)

n = 14

for a one-independent sample t-test

DF = Degrees of Freedom

DF = n - 1

DF = 14 - 1

DF = 13

Part b)

df₁ = 15, n₂ = 25

for a two-independent sample t-test

DF = df₁ +df₂

df₁ = 15,

df₂ = n₂ - 1 = 25-1 = 24,

Thus

DF = df₁ +df₂

DF = 15 + 24

DF = 39

Part c)

critical value = 63.657 for a two-tailed test,

α = 0.01

Look in t table for two tail area = 0.01 column and find 63.657 in that column and then find corresponding DF

63.657 = 63.66 which corresponds to df =1

thus

DF = 1

Part d)

critical value = 1.645 for a one-tailed test,

α = 0.05

Look in t table for one tail area = 0.05 column and find 1.645 in that column and then find corresponding DF

t = 1.645 corresponds to infinity

thus

DF = INFINITY