Answer:
43 < μ₁ - μ₂ < 49
Step-by-step explanation:
Sample 1:
Mean x₁ = 88
Sample size n₁ = 173
Sample standard deviation s₁ = 12,22
Sample 2:
Mean x₂ = 53,5
Sample size n₂ = 127
Sample standard deviation s₂ = 13,59
CI 95 % α = 5% α = 0,05 α/2 = 0,025
We need to find:
( x₁ - x₂ ) - tα/2,v *√ (s₁²/n₁ ) + (s₂²/n₂) < μ₁ - μ₂ < ( x₁ - x₂ ) + tα/2,v *√ (s₁²/n₁ ) + (s₂²/n₂)
v = degree of fredom
v = [ ( s₁²/n₁ + s₂²/n₂)² / (s₁²/n₁)² /n₁-1 + (s₂²/n₂)²/n₂-1
v = [ (0,86 + 1,45 ) / 0,0043 + 0,017
v = 2,31 / 0,0213
v = 108
Then t 0,025, 108 from t table is: We will take v = 100
t = 1,984
Now
√ (s₁²/n₁ ) + (s₂²/n₂) = √ 0,86 + 1,43
√ 2,3 = 1,51
Then: CI:
(173 - 127 ) - 1,984*1,51 < μ₁ - μ₂ < ( 173 - 127 ) + 1,984*1,51
46 - 3 < μ₁ - μ₂ < 46 + 3
43 < μ₁ - μ₂ < 49
