Two Independent pooled samples Mean -- Hypothesis and C.I.

Two Independent samples' pooled Means hypothesis test (2-Samp T-Test) and confidence intervals (2 Samp T-Int)

Assuming populations' variances are equal: σ₁²=σ₂². i.e. pooled.
Also that the data is normal (but robust to minor non-normality, less so to skewed).
H₀: samples from populations with same means, μ₁=μ₂

H₀: μ₁ = μ₂
Choose one:
H_A: μ₁ < μ₂	"H_A < H₀"	Left-tailed
H_A: μ₁ > μ₂	"H_A > H₀"	Right-tailed
H_A: μ₁ ≠ μ₂	"H_A ≠ H₀"	Two-tailed

Independent samples data:
X1:
X2:

n₁:    n₂:
x̄₁:    x̄₂:      x̄₁-x̄₂:
s₁:    s₂:
s_p pooled stdev:
pooled standard error =s_p√(1/n₁+1/n₂):
df=n₁+n₂-2:
maxVarRatio=max(s₁²,s₂²) / min(s₁²,s₂²)
F p-value= FCDF(maxVarRatio, n₁-1,n₂-1) should be ≥ 0.05
t:
T Test compares "signal" (x̄₁-x̄₂) to "noise" of the pooled standard error. If the two x̄'s are the same, then t=0 and p-value=1.

p-value (TCDF(t)):

E = t_c * s_p * √(1/n₁+1/n₂)

Confidence intervals for the true mean difference:

There is a CL% chance that [(x̄₁-x̄₂)-E, (x̄₁-x̄₂)+E] contains the true difference in means.