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

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

Are the two samples from the same or different "populations", e.g. control/placebo and treatment/intervention.

Assuming populations' variances are not equal. i.e. not pooled.
σ's unknown and not assumed equal.
Samples sizes should be either >30 or from a normal population. Robust against some departure from normality for small n's.

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: can be different sizes
X1:
X2:

OR Enter the n, x̄, and s for each sample:
n₁:    n₂:
x̄₁:    x̄₂:      x̄₁-x̄₂:
s₁:    s₂:

Choose method of determing degrees of freedom (df):
Welch-Satterthwaite OR Min(n₁-1,n₂-1)

A=s²₁/n₁: B=s²₂/n₂:
df:
t: Critical value: α=0.05: α=0.01:

p-value (TCDF(t)):

E = t_c * √(A+B)

Confidence intervals for the difference between the populations' means:

** For one-tailed tests use 90% CL for α=.05 and 98% CL for α=.01
There is a CL% chance that [(x̄₁-x̄₂)-E, (x̄₁-x̄₂)+E] contains the true difference between the populations' means.
** If CI does not contain 0, reject H₀.
** If CI contains 0, fail to reject H₀.

heights
1698 1727 1734 1684 1667 1680 1785 1885 1841 1702 1738 1732
1810 1850 1777 1811 1780 1733 1814 1861 1709 1740 1694 1766 1748 1794 1780

handwashing  Bacteria counts
soap: n=55 mean=69 s=106
alcohol: n=59 mean=35 s=59

second-hand smoke.  cotinine
exposed: n=40 mean=60.58 s=138.08
not exposed: n=40 mean=16.35 s=62.53

weights
76.9 85.2 97.9 69.4 71.2 77.7 78.2 75.6 84.4 72.0 60.6 83.0
79.2 91.5 96.5 67.5 107.3 79.3 78.2 88.2 71.5 94.7 66.5 87.9 67.5 88.4 69.5


CholesterolLevel ofHeartAttackPatients
270 236 210 142 280 272 160 220 226 242 186 266 206 318 294 282 234 224 276 282 360 310 280 278 288 288 244 236 
CholesterolLevel ofHealthyIndividual
196 232 200 242 206 178 184 198 160 182 182 198 182 238 198 188 166 204 182 178 212 164 230 186 162 182 218 170 200 176

Sodium in Beef Hotdogs
495 477 425 322 482 587 370 322 479 375 330 300 386 401 645 440 317 319 298 253 
Sodium in Poultry Hotdogs
430 375 396 383 387 542 359 357 528 513 426 513 358 581 588 522 545 430 375 396


men-women difference in facial memory.
men:
3 6 8 5 6 6 6 5 3 3 8 6 9 5 4 5 6 6 8 5 8 7 7 6 7
women:
8 8 7 8 9 10 8 8 9 10 7 9 8 9 8 9 8 8 7 9 6 7 9 7 8