Connect the ideas.
- State the target population, sampling frame and design.
- Sample-mean standard error is population standard deviation divided by the square root of sample size.
- Use a justified sampling distribution and distinguish exact from approximate normality.
- An interval is an estimate plus or minus critical value times standard error.
- Confidence describes repeated coverage of a fixed parameter, not a proportion of individual measurements.
- For a data-based proportion interval, use the observed proportion to estimate standard error.
- Larger samples usually improve precision but do not cure bias.
- Round required sample sizes upwards and report limitations.
Put it together.
Choose a paper and show your working.
Sampling and confidence intervals — Paper 1
Build from sampling design to normal models, interval estimation and interpretation. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assistedSampling and confidence intervals — Paper 2
Interpret study records, recover missing quantities and compare estimation procedures. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assistedSampling and confidence intervals — Paper 3
A community transport project combines survey design, estimates and careful reporting. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assistedSampling and confidence intervals — Paper 4
Evaluate uncertainty in production and quality-assurance studies. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assistedSampling and confidence intervals — Paper 5
Work backwards from intervals and compare precision under different designs. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assistedSampling and confidence intervals — Paper 6
Combine model checks, inverse calculations and applied evaluation in a demanding review. Use supplied two-sided critical values: 90% 1.645, 95% 1.96, 98% 2.326 and 99% 2.576. Retain intermediate precision; give final probabilities to four decimal places and state assumptions.
10 questions · 60 marks · 75 minutes · Technology-assisted
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Mathematical Methods: sampling distributions and confidence intervals for means and proportions. Mean tasks distinguish known population spread from sufficiently large-sample estimated-spread normal intervals. Repeated-interval computational simulation, approximation conditions, design and interpretation are included.
Official curriculum source ↗