S3.3.6 - Central Limit theorem for sample means

Use of Central Limit theorem to X −µ can be treated as N(0, 1) when n is large. extend hypothesis tests and S / n confidence intervals to samples from non-Normal distributions.; Use A knowledge of the t-distribution is not required. of large sample results to extend to the case in which the variance is unknown.

Use central limit theorem for sample means to connect the rule to the data and decision in the question.

This matters because central limit theorem for sample means determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply central limit theorem for sample means to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Central Limit theorem for sample means is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.