Chi-squared tests — AS & A Level Further Mathematics (9231) questions by topic
Goodness-of-fit and independence testing anchor this topic: testing whether eye colours are uniformly distributed against a survey of 120 people, testing whether three bus companies' punctuality differs, and testing germination counts across 150 plant pots against an expected distribution.
Show, test, carry out, complete and calculate lead the command words across 16 questions from 2023 to 2025 papers, worth 6 to 10 marks, where combining cells with low expected frequencies before calculating is essential. Working through each expected-frequency table and chi-squared statistic with instant marking flags an uncombined pair of low-frequency cells or an inconsistent tabular value before the conclusion is drawn on faulty grounds.
What examiners look for
- A recurring criticism is not working to enough accuracy for a 'show that' result, when candidates were expected to work exactly, in fractions, or to at least 5 decimal places.
- Examiners note not combining the first two columns was a common gap, necessary because the first expected frequency was below 5.
- A common mistake stated the null hypothesis with insufficient detail, such as 'it is a good fit model', rather than referring to both the distribution and the data.
- Reports flag combining one pair of columns but not the other, leaving some expected frequencies still below 5.
- Strong scripts correctly pooled both pairs of cells, applied the chi-squared formula, and chose the tabular value consistent with 6 degrees of freedom.
May–June 2025, Paper 41
Eggs in a supermarket are sold in boxes of six. A supermarket manager wishes to model the number of broken eggs in the boxes sold in the store. A random sample of 2000 boxes is…
Answer this question and get it marked →May–June 2025, Paper 42
Eggs in a supermarket are sold in boxes of six. A supermarket manager wishes to model the number of broken eggs in the boxes sold in the store. A random sample of 2000 boxes is…
Answer this question and get it marked →May–June 2025, Paper 43
A person's eye colour may be categorised as "brown", "blue" or "other". A scientist claims that these eye colours are uniformly distributed and hence are equally likely to occur…
Answer this question and get it marked →May–June 2025, Paper 44
A shop selling electrical goods has a team of three salespeople: Avril, Ben and Charlie. The manager wishes to investigate whether the salespeople are equally successful at…
Answer this question and get it marked →May–June 2024, Paper 41
Two companies, P and Q, produce a certain type of paint brush. An independent examiner rates the quality of the brushes produced as poor, satisfactory or good. He takes a random…
Answer this question and get it marked →May–June 2024, Paper 42
Two companies, P and Q, produce a certain type of paint brush. An independent examiner rates the quality of the brushes produced as poor, satisfactory or good. He takes a random…
Answer this question and get it marked →May–June 2024, Paper 43
There are three bus companies in a city. The council is investigating whether the buses reliably arrive at their destination on time. The results from random samples of buses from…
Answer this question and get it marked →October–November 2024, Paper 41
A statistician believes that the number of telephone calls received by an advice centre in a 10-minute interval can be modelled by the Poisson distribution Po(1.9). The number of…
Answer this question and get it marked →October–November 2024, Paper 42
Rosie sows 5 seeds in each of 150 plant pots. The number of seeds that germinate is recorded for each pot. The results are summarised in the following table. Number of seeds that…
Answer this question and get it marked →October–November 2024, Paper 43
A statistician believes that the number of telephone calls received by an advice centre in a 10-minute interval can be modelled by the Poisson distribution Po(1.9). The number of…
Answer this question and get it marked →May–June 2023, Paper 41
A random sample of 50 values of the continuous random variable X was taken. These values are summarised in the following table. Interval 1 <= x < 1.5 1.5 <= x < 2 2 <= x < 2.5 2.5…
Answer this question and get it marked →May–June 2023, Paper 42
A random sample of 50 values of the continuous random variable X was taken. These values are summarised in the following table. Interval 1 <= x < 1.5 1.5 <= x < 2 2 <= x < 2.5 2.5…
Answer this question and get it marked →May–June 2023, Paper 43
A scientist is investigating whether the ability to remember depends on age. A random sample of 150 students in different age groups is chosen. Each student is shown a set of 20…
Answer this question and get it marked →October–November 2023, Paper 41
A town council has published its plans for redeveloping the town centre and residents are being asked whether they approve or disapprove. A random sample of 250 responses has been…
Answer this question and get it marked →October–November 2023, Paper 42
The number of breakdowns on a particular section of road is recorded each day over a period of 90 days. It is suggested that the number of breakdowns follows a Poisson…
Answer this question and get it marked →October–November 2023, Paper 43
A town council has published its plans for redeveloping the town centre and residents are being asked whether they approve or disapprove. A random sample of 250 responses has been…
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