Question

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

(a) n = 24 for a one-independent sample t-test


(b) df₁ = 12, n₂ = 21 for a two-independent sample t-test


(c) critical value = 1.645 for a one-tailed test, α = 0.05

(d) critical value = 63.657 for a two-tailed test, α = 0.01

Answer 1

Part a)

Number of observations n = 24

for one sample t-test we have (n-1) degrees of freedom as we are estimating only one parameter.

So answer = 23

Part b)

n1 = 12, n2 = 21

For two sample t- test we (n1+n2-2) degrees of freedom as we are estimating two sample means.

So answer 21+12-2= 31

Part c)

critical value 1.645 alpha level 0.05 one tail test.

1.645 is the value of z score and 5 % level of significance , Hence we can not determine the degrees of freedom so here we have infinite degrees of freedom.

Part d)

critical value = 63.657 for a two-tailed test, α = 0.01

For this test degrees of freedom is 1.
(reviewed from t table)