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, $1 = 5.0, 52 = 6.0 (b) m = 12, n = 18, S, = 5.0, S2 = 6.0 (c) m = 12, n = 18,51 = 3.0, 52 = 6.0 (d) m = 10, n = 21, S, = 5.0, S2 = 6.0

Answer 1

Answer:

Given,

To give the degree of freedom

Consider,

degree of freedom = (s1^2/m + s2^2/n)^2 / (s1^4 / (m^2(m-1)) + s2^4 / (n^2(n-1))) ------------> (1)

a)

Here m = 12 , n = 15 , s1 = 5 , s2 = 6

Substitute values in (1)

df = (5^2/12 + 6^2/15)^2 / (5^4 / (12^2(12-1)) + 6^4 / (15^2(15-1)))

= 16.483

= 17

b)

m = 12 , n = 18 , s1 = 5 , s2 = 6

Substitute values in (1)

Then we get

df = 26.47173

= 27

c)

m = 12 , n = 18 , s1 = 3 , s2 = 6

Substitute values in (1)

Then we get

df = 26.40256709

= 26

d)

m = 10 , n = 21 , s1 = 5 , s2 = 6

Substitute values in (1)

Then we get

df = 21.10834119

= 21