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In: Statistics and Probability

Determine the number of degrees of freedom for the two-sample t test or CI in each...

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 = 10, s1 = 5.0, s2 = 6.0


(b)    m = 12, n = 18, s1 = 5.0, s2 = 6.0


(c)    m = 12, n = 18, s1 = 3.0, s2 = 6.0


(d)    m = 10, n = 24, s1 = 5.0, s2 = 6.0

Solutions

Expert Solution

SOLUTION:

From given data,

Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations.

(a)    m = 12, n = 10, s1 = 5.0, s2 = 6.0

df = [ / + / ]2 / [( / )2 / ( -1 ) + ( / )2 / ( -1 ) ]

df = [ 5.02 / 12 + 6.02 / 10 ]2 / [( 5.02 / 12  )2 / (12 -1 ) + (6.02 / 10 )2 / (10​​​​​​​ -1 ) ]

df =32.300278 / [0.394570 +1.44]

df =32.300278 /1.83457

df =17.606

df =18 (Round your answers down to the nearest whole number.)

(b)    m = 12, n = 18, s1 = 5.0, s2 = 6.0

df = [ / + / ]2 / [( / )2 / ( -1 ) + ( / )2 / (​​​​​​​ -1 ) ]

df = [ 5.02 / 12 + 6.02 / 18 ]2 / [( 5.02 / 12  )2 / (12 -1 ) + (6.02 / 18 )2 / (18​​​​​​​ -1 ) ]

df =16.67361 /[ 0.3945707 +0.235294]

df =16.67361 /0.6298647

df =26.4717327

df =27 (Round your answers down to the nearest whole number.)

(c)    m = 12, n = 18, s1 = 3.0, s2 = 6.0

df = [ / + / ]2 / [( / )2 / ( -1 ) + ( / )2 / (​​​​​​​ -1 ) ]

df = [ 3.02 / 12 + 6.02 / 18 ]2 / [( 3.02 / 12  )2 / (12 -1 ) + (6.02 / 18 )2 / (18​​​​​​​ -1 ) ]

df =7.5625 /[ 0.051136 +0.2352941]

df =7.5625 /0.2864301

df =26.4026022

df =27 (Round your answers down to the nearest whole number.)

(d)    m = 10, n = 24, s1 = 5.0, s2 = 6.0

df = [ / + / ]2 / [( / )2 / ( -1 ) + ( / )2 / (​​​​​​​ -1 ) ]

df = [ 5.02 / 10 + 6.02 / 24 ]2 / [( 5.02 / 10  )2 / (10 -1 ) + (6.02 / 24 )2 / (24​​​​​​​ -1 ) ]

df =16 /[ 0.6944 +0.09782608]

df =16 /0.79222608

df =20.196255

df =20 (Round your answers down to the nearest whole number.)

orchestra answered 2 years ago
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