Year 10
Choose sampling methods carefully, justify why randomness matters, investigate claims using appropriate data representations, and interpret results of statistical tests.
Statistics and data — sampling and inference
**Sampling** is selecting a subset of a population to study. A **random sample** (e.g., random number generator) reduces bias; a **systematic sample** (e.g., every 10th person) is also often good. **Biased sampling** (e.g., convenience sampling) can lead to misleading conclusions. A **hypothesis** is a claim about a population. We test it using sample data: does the sample provide evidence for or against the claim? If observed data is very unlikely under the null hypothesis, we reject it. Sample statistics estimate population parameters: sample mean estimates population mean, sample proportion estimates population proportion.
Identifying biased vs unbiased sampling
A school wants to survey student satisfaction. Method A: ask 50 volunteers at lunch. Method B: randomly select 50 student ID numbers from the register. Which is biased?
Volunteer and convenience samples are often biased. Random samples reduce systematic bias.
Testing a hypothesis using a sample
A company claims that 80% of customers are satisfied. A survey of 100 customers finds 75 satisfied. Is this consistent with the claim?
Large differences (relative to sample size and variability) suggest the hypothesis should be questioned.
Using data representations to investigate a claim
A claim: 'Boys are taller than girls.' Samples give: boys min=140, Q1=155, median=163, Q3=170, max=185 (cm). Girls min=130, Q1=140, median=148, Q3=155, max=170 (cm).
The claim is supported if the distributions are significantly different in centre (median) and less so in spread.
A manufacturer claims that its light bulbs last an average of 1000 hours. A sample of 50 bulbs is tested. Results: mean 980 hours, standard deviation 50 hours. Investigate whether this claim is reasonable.
Always consider: Is the sample random and representative? What is the size? Does it support or contradict the claim? Use data representations to visualise the comparison.
Which sampling method is most likely to be biased?
💡 Convenience sampling picks easily accessible subjects, often missing important groups.
A claim is tested with a sample of n = 1000 instead of n = 50. How does this change affect our confidence?
💡 Larger samples give more stable estimates and reduce uncertainty.
A hypothesis test result shows the sample data is very unlikely if the null hypothesis is true. What should we do?
💡 If observed data is very unlikely under the hypothesis, the hypothesis is not supported.
A survey of 100 people finds 52 in favour, 48 against. Is this strong evidence of a preference?
💡 With samples of this size, a 52-48 split is well within normal variation for a 50-50 population.
Which type of graph is best for comparing distributions of two groups?
💡 Box plots show medians, quartiles and outliers, making group comparison easy.
Watch for these when working through the lesson.
These ideas fit closely with this lesson.