Interpreting and justifying claims with a confidence interval for a proportion

What the exam asks

Under Practice 4 (Interpret Results), the exam asks you to:

Interpret a $C\%$ confidence interval in context.
Interpret the confidence level $C\%$ in the context of repeated sampling.
Justify a claim about a population proportion $p$ using the interval.
Determine how changing the confidence level $C$ or sample size $n$ affects the critical value $z^*$ , margin of error, and interval width.

Students frequently confuse interpreting the interval with interpreting the level. Keep them strictly separate using these templates:

What to interpret	Required components	Exam-ready template
Confidence Interval	Confidence level, endpoints, parameter (population proportion) in context.	“We are $C\%$ confident that the interval from $a$ to $b$ captures the population proportion of [context].”
Confidence Level	Repeated random sampling of the same size $n$ , long-run capture rate, parameter in context (no specific numbers and ).

A confidence interval is a set of plausible values for the population proportion $p$ .

Claim that $p$ equals a specific value ( $p = p_0$ ): If $p_0$ is the interval, is a plausible value, so there is convincing statistical evidence against the claim. If is the interval, it is implausible, providing convincing statistical evidence against .