Answer:
a) σ = 4933,64
b) CI 99% = ( - 5746 ; 7194 )
c) No difference in brands
Step-by-step explanation:
Brand 1:
n₁ = 8
x₁ = 38222
s₁ = 4974
Brand 2:
n₂ = 8
x₂ = 37498
s₂ = 4893
As n₁ = n₂ = 8 Small sample we work with t -student table
degree of freedom df = n₁ + n₂ - 2 df = 8 +8 -2 df = 14
CI = 99 % CI = 0,99
From t-student table we find t(c) = 2,624
CI = ( x₁ - x₂ ) ± t(c) * √σ²/n₁ + σ²/n₂
σ² = [( n₁ - 1 ) *s₁² + ( n₂ - 1 ) * s₂² ] / n₁ +n₂ -2
σ² = 7* (4974)² + 7*( 4893)² / 14
σ² = 24340783 σ = 4933,64
√ σ²/n₁ + σ²/n₂ = √ 24340783/8 + 24340783/8
√ σ²/n₁ + σ²/n₂ = 2466
CI 99% = ( x₁ - x₂ ) ± 2,624* 2466
CI 99% = 724 ± 6470
CI 99% = ( - 5746 ; 7194 )
As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups
