Define and frame
With s=12 and n=36 compute the estimated SE of the mean and explain how it differs from SD.
Scenario: Suppose a sample has standard deviation 12 and sample size 36. How precisely is its mean estimated?
Use the fictional dataset if the question refers to it. Always show your reasoning; an exact number without context is not enough. The four written tasks are teacher-assessed. The self-check below is formative and does not affect the 20-mark assignment.
Written problem set
Calculate or apply
If n increases from 36 to 144 with s unchanged, how does SE change? Calculate the new value.
Evaluate the design
State the long-run coverage interpretation of a 95% confidence interval, avoiding a literal probability claim about the fixed parameter inside one observed interval.
Interpret and communicate
Why may a narrow confidence interval from a large unrepresentative volunteer sample still lack external validity?
Standard scoring guide
Each written task is worth 5 points: correct key idea (2), justified application or computation (2), and a clear statement with limits (1). This original rubric is not official UCL assessment.
Formative self-check · 4 questions
Choose one answer for each item, then check the feedback. Answers and explanations are available on this public study page; the separate written-task instructor key is private.