Two-Sample T-Test Visualization (Group 1 vs. Group 2) | \(H_0: \mu_1 = \mu_2\) vs. \(H_a: \mu_1 \neq \mu_2\)

Significance Level (α)

Group 1 (e.g., New Process)

Sample Mean (x̄₁)
Standard Deviation (s₁)
Sample Size (n₁)

Group 2 (e.g., Old Process)

Sample Mean (x̄₂)
Standard Deviation (s₂)
Sample Size (n₂)
T-Statistic Calculation
\[\frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\]
=
\[\frac{280 - 270}{\sqrt{\frac{35^2}{30} + \frac{30^2}{30}}}\]
=
1.1547

Group 1 has higher sample mean

Degrees of Freedom (Welch's): 57.02

Welch-Satterthwaite Formula:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

This adjusts for unequal variances and sample sizes between groups.
p-value: 0.2530 (Not Significant at α = 0.05)

A two-tailed p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one we got in either direction. It helps distinguish if the improvement is likely real (signal) or just random chance (noise). The selected significance level (α) determines the threshold for rejecting the null hypothesis.

The t-test is computed from the specified summary statistics, not from the simulated sample shown. In real life, you don't get to change one input at a time (increase the sample size, but keep the sample mean and sample standard deviation the same).