A large sample of 40 units has a mean 5.22 and a standard deviation σ of 2.31
Another large sample of 40 related units has a mean 4.44 and a standard deviation σ of 1.74
Construct a 90% confidence interval for the difference between the means μ₁ - μ₂

Confidence Interval Formula for μ₁ - μ₂ is as follows:
(x₁ - x₂) - zscore_α x √a < μ₁ - μ₂ < (x₁ - x₂) + zscore_α x √a where:
x₁ = sample mean 1, x₂ = sample mean 2, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2
and a is denoted below
Calculate α:
α = 1 - Confidence%
α = 1 - 0.9
α = 0.45726633377059

Find α spread range:
α = ½(α)
α = ½(0.45726633377059)
α = 0.05

Find z-score for α value for 0.05
zscore_0.05 = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

Calculate a:

a = √0.1334025 + 0.07569
a = √0.2090925
a = 0.45726633377059

Calculate high end confidence interval total:
High End = (x₁ - x₂) + zscore_α x √a
High End = (5.22 - 4.44) + 1.645 x 0.45726633377059
High End = 0.78 + 0.75220311905263
High End = 1.5322

Calculate low end confidence interval total:
Low End = (x₁ - x₂) - zscore_α x √a
Low End = (5.22 - 4.44) - 1.645 x 0.45726633377059
Low End = 0.78 - 0.75220311905263
Low End = 0.0278

Now we have everything, display our 90% confidence interval:
0.0278 < μ₁ - μ₂ < 1.5322
What this means is if we repeated experiments, the proportion of such intervals that contain μ₁ - μ₂ would be 90%