Sampling and confidence intervals.
Build defensible sampling models, construct mean and proportion confidence intervals, and explain precision and limitations.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Random sampling and bias
Choose a defensible sample and recognise bias that a larger sample cannot repair.
- 02
Sample means and the central-limit idea
Describe repeated sample means and decide when their distribution can be modelled as normal.
- 03
Standard error
Separate individual variation from uncertainty in the estimated mean.
- 04
Confidence intervals for a population mean
Construct a normal confidence interval for a mean with stated known population spread.
- 05
Confidence level and interpretation
Interpret confidence through repeated samples and avoid claims about individual measurements.
- 06
Effect of sample size and variability
Predict precision changes caused by sample size, variability and confidence level.
- 07
Population/sample proportions
Calculate a sample proportion and distinguish it from the population parameter.
- 08
Sampling distribution of a sample proportion
Model the sampling variation of a proportion and assess normal-approximation conditions.
- 09
Confidence intervals for a population proportion
Construct a normal-approximation proportion interval and report its limitations.
- 10
Margin of error and sample-size calculations
Plan sample size for a specified margin, using a stated mean spread or planning proportion.
- 11
Assessing claims and limitations
Evaluate what an interval supports and what the study cannot establish.
Topic review
Revisit the key ideas, then choose a practice paper.