One-sample and two-sample mean tests

Learning objectives

• Choose between one-sample and two-sample t-tests.
• Check assumptions and report the effect interval.
• Recognise when Welch’s method is appropriate.

Structure

• One-sample H0: μ = target.
• Two-sample H0: μ1 − μ2 = 0.
• Independent observations; representative samples.
• Welch’s method when variances differ.

Garment-factory example

Test whether mean SPI meets the standard, or compare average operation time between two independent methods with N=30 per group.

Method

1. Plot the data and check independence.
2. Compute t, p-value and CI in a spreadsheet.
3. Report the estimated difference with units.
4. Compare the effect with the practical threshold.

Common mistakes

• Using a two-sample test on paired garments.
• Ignoring subgroup and time structure.