Answer:
We accept H₀ we don´t have evidence of differences between the two toothbrushes
Step-by-step explanation:
Toothbrushes A
Sample mean μₐ = 119,7
Standard deviation sₐ = 1,74
Sample size nₐ = 18
Toothbrushes B
Sample mean μ₀ = 120,6
Standard deviation s₀ = 1,72
Sample size n₀ = 15
With CI = 90 % CI = ( -1,93 ; 0,13 ) that s the acceptance region for H₀
Test hypothesis is
H₀ μₐ = μ₀
Hₐ μₐ ≠ μ₀
We need to calculate t(s) as
t(s) = ( μₐ - μ₀ ) /Sₓ * √ (1/nₐ) + 81/n₀)
and see if it is insde CI
Sₓ = (nₐ - 1 ) * sₐ² + ( n₀ - 1 ) * s₀² / nₐ + n₀ - 2
Sₓ = 17*3,03 + 14*2,96 / 31
Sₓ = (51,51 + 41,44 )/ 31
Sₓ = 2,998
t(s) = 0,9 / 2,998*√(1/18) + (1/15)
t(s) = 0,9 / 1,04
t(s) = 0,87
