Question

Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)

(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

Answer 1

a

`df = 24.32`

b

`df = 30.10`

c

`df = 30.7`

d

`df = 25.5`

Explanation:

Generally degree of freedom is mathematically represented as

`df = ( [( s^2_i )/(m) + ( s^2_j )/(n) ]^2 )/( ( [ (s^2_i)/(m) ]^2 )/(m-1 ) +( [ (s^2_j)/(n) ]^2 )/(n-1 ) )`

Considering a

a) m = 12, n = 15, s1 = 4.0, s2 = 6.0

`df = ( [( 4^2 )/(12) + ( 6^2 )/(15) ]^2 )/( ( [ (4^2)/(12) ]^2 )/(12-1 ) +( [ (6^2)/(15) ]^2 )/(15-1 ) )`

`df = 24.32`

Considering b

(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0

`df = ( [( 4^2 )/(12) + ( 6^2 )/(21) ]^2 )/( ( [ (4^4)/(12) ]^2 )/(12-1 ) +( [ (6^2)/(21) ]^2 )/(21-1 ) )`

`df = 30.10`

Considering c

(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0

`df = ( [( 3^2 )/(12) + ( 6^2 )/(21) ]^2 )/( ( [ (3^4)/(12) ]^2 )/(12-1 ) +( [ (6^2)/(21) ]^2 )/(21-1 ) )`

`df = 30.7`

Considering c

(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

`df = ( [( 4^2 )/(10) + ( 6^2 )/(24) ]^2 )/( ( [ (4^2)/(10) ]^2 )/(10-1 ) +( [ (6^2)/(24) ]^2 )/(24-1 ) )`

`df = 25.5`