Sampling and confidence intervals — Topic Review | Year 12

QUICK RECAP

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.

Practice tests

Complete each paper and show your working.

Sampling and confidence intervals — Paper 1
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide
Sampling and confidence intervals — Paper 2
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide
Sampling and confidence intervals — Paper 3
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide
Sampling and confidence intervals — Paper 4
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide
Sampling and confidence intervals — Paper 5
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide
Sampling and confidence intervals — Paper 6
10 questions · 60 marks · 75 minutes · Technology-assisted
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.
Open test Marking guide

Back to Sampling and confidence intervals

Connect the ideas

Practice tests

Sampling and confidence intervals — Paper 1

Sampling and confidence intervals — Paper 2

Sampling and confidence intervals — Paper 3

Sampling and confidence intervals — Paper 4

Sampling and confidence intervals — Paper 5

Sampling and confidence intervals — Paper 6