S3.3.8 - Use of large sample results

Use of large sample results to (X −Y)−(µ −µ) Use of x y ∼ N(0, 1). extend to the case in which the S2 S2 population variances are unknown. x + y n n x y A knowledge of the t-distribution is not required.

Use use of large sample results to connect the rule to the data and decision in the question.

This matters because use of large sample results determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply use of large sample results to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Use of large sample results is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.