Hypothesis tests — AS & A Level Mathematics (9709) questions by topic
Testing whether worm lengths differ from a stated mean, checking if a river pollutant's concentration falls below a permitted level from 50 sampled readings, and testing a claimed change in the proportion of job applicants with first-class degrees are typical of the 13 hypothesis test questions from 2023 to 2025, worth 5 to 12 marks.
Carry out and find lead the command words, with state, explain and comment used to set out hypotheses and interpret a conclusion in context. Because a hypothesis test is marked on the full chain from hypotheses through test statistic to conclusion, submit your working for instant marking, so a wrongly stated null hypothesis or a one-tailed versus two-tailed slip is caught before it invalidates the whole test.
May–June 2025, Paper 61
A manufacturer of cell phones claims that 25% of students own a Pumpkin phone. Jeyeraj thinks that the proportion of students at his large college who own a Pumpkin phone is less…
Answer this question and get it marked →May–June 2025, Paper 63
The lengths of pencils made at a factory are normally distributed. The standard deviation of the lengths is sigma cm, and the mean is supposed to be 10 cm. An inspector thinks…
Answer this question and get it marked →In the past, one quarter of job applicants at a certain firm had first-class degrees. A change is made in the job description and a director of the firm believes that, on average,…
Answer this question and get it marked →May–June 2025, Paper 65
A firm makes a certain type of battery-powered toy. The battery life is denoted by X hours and the population mean of X is supposed to be 12. The Quality Control department wished…
Answer this question and get it marked →October–November 2024, Paper 61
The lengths, in centimetres, of worms of a certain kind are normally distributed with mean mu and standard deviation 2.3. An article in a magazine states that the value of mu is…
Answer this question and get it marked →October–November 2024, Paper 62
A factory owner models the number of employees who use the factory canteen on any day by the distribution B(25, p). In the past the value of p was 0.8. A new menu is introduced in…
Answer this question and get it marked →The heights of one-year-old trees of a certain variety are known to have mean 2.3 m. A scientist believes that, on average, trees of this age and variety in her region are…
Answer this question and get it marked →October–November 2024, Paper 63
The lengths, in centimetres, of worms of a certain kind are normally distributed with mean mu and standard deviation 2.3. An article in a magazine states that the value of mu is…
Answer this question and get it marked →May–June 2023, Paper 61
In the past, the annual amount of wheat produced per farm by a large number of similar sized farms in a certain region had mean 24.0 tonnes and standard deviation 5.2 tonnes. Last…
Answer this question and get it marked →October–November 2023, Paper 61
A biologist wishes to test whether the mean concentration mu, in suitable units, of a certain pollutant in a river is below the permitted level of 0.5. She measures the…
Answer this question and get it marked →October–November 2023, Paper 62
A researcher read a magazine article which stated that boys aged 1 to 3 prefer green to orange. It claimed that, when offered a green cube and an orange cube to play with, a boy…
Answer this question and get it marked →The height H, in metres, of mature trees of a certain variety is normally distributed with standard deviation 0.67. In order to test whether the population mean of H is greater…
Answer this question and get it marked →October–November 2023, Paper 63
A biologist wishes to test whether the mean concentration mu, in suitable units, of a certain pollutant in a river is below the permitted level of 0.5. She measures the…
Answer this question and get it marked →Other AS & A Level Mathematics topics
- Differentiation (95)
- Algebra, logarithmic and exponential functions (87)
- Trigonometry (57)
- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Sampling and estimation (28)
- Permutations and combinations (27)