S3.3.7 - Hypothesis test for the difference

Hypothesis test for the difference (X −Y)−(µ −µ) between the means of two Normal x y Use of ∼ N(0, 1). distributions with variances known. σ2 σ2 x + y n n x y.

Use hypothesis test for the difference to connect the rule to the data and decision in the question.

This matters because hypothesis test for the difference determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply hypothesis test for the difference to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Hypothesis test for the difference is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.