Hypothesis tests: past paper questions

Where the questions come from

• Question 2May/June 2026, paper 61Structured5 marks

  In the past, $2\mathrm{\%}$ of talking dolls made by a certain firm have been faulty. Following a change in the manufacturing process, a quality control officer suspects that the percentage of faulty talking dolls has increased.

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• Question 2Oct/Nov 2025, paper 61Structured8 marks

  The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, $x$ grams, of each packet.

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• Question 5Oct/Nov 2024, paper 61Structured6 marks

  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 12.7. A scientist wishes to test whether this value is correct.

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• Question 5Oct/Nov 2023, paper 61Structured5 marksHas a diagram

  In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution $\mathrm{P}\mathrm{o}(0.31)$. Following a change in the position of the desk, it is expected that the mean number of enquiries per minute will increase.

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• Question 4May/June 2026, paper 61Structured11 marks

  The score on one spin of a 5-sided spinner is denoted by the random variable $X$ with probability distribution as shown in the table.

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• Question 5Oct/Nov 2025, paper 61Structured6 marks

  It is known that $20\mathrm{\%}$ of households in a certain country contain more than 4 people. Laxmi believes that, in her town, the percentage is lower than $20\mathrm{\%}$. She chooses a random sample of 40 households in her town and notes the number which contain more than 4 people.

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• Question 7Oct/Nov 2024, paper 61Structured14 marks

  The number of accidents per year on a certain road has the distribution $\mathrm{P}\mathrm{o}(\lambda )$. In the past the value of $\lambda$ was 3.3. Recently, a new speed limit was imposed and the council wishes to test whether the value of $\lambda$ has decreased.

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• Question 7Oct/Nov 2023, paper 61Structured12 marksHas a diagram

  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 concentration, $x$, of the pollutant at 50 randomly chosen locations in the river.

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• Question 3May/June 2026, paper 62Structured6 marks

  The number of vehicles, $X$, passing a certain junction between 1.00 pm and 1.01 pm is modelled by a Poisson distribution. In the past, the population mean of $X$ was 2.4. After a change is made to the junction, the value of $X$ is noted on a randomly chosen day.

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• Question 4Oct/Nov 2025, paper 62Structured7 marks

  An inspector believes that 18% of cups made at a certain factory contain flaws. The factory owner claims that the true percentage is less than 18%. The inspector examines a random sample of 40 cups and finds that 3 of them contain flaws.

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• Question 3Oct/Nov 2024, paper 62Structured6 marks

  A factory owner models the number of employees who use the factory canteen on any day by the distribution $\mathrm{B}(25,p)$. In the past the value of $p$ was 0.8. A new menu is introduced in the canteen and the owner wants to test whether the value of $p$ has increased.

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• Question 3Oct/Nov 2023, paper 62Structured9 marks

  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 is more likely to choose the green one. The researcher disagrees with this claim.

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• Question 6May/June 2026, paper 62Structured9 marks

  The length of time, $T$ minutes, that customers spend in a certain shop has the distribution $\mathrm{N}(\mu ,9.2)$. Last year the value of $\mu$ was 12.4. The manager of the shop wants to test whether the value of $\mu$ has decreased this year.

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• Question 6Oct/Nov 2025, paper 62Structured12 marks

  The weekly profit, in dollars, made by a certain firm has a normal distribution. In the past, the weekly profit had the distribution $\mathrm{N}(736,{26}^2)$.

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• Question 7Oct/Nov 2024, paper 62Structured9 marks

  The heights of one-year-old trees of a certain variety are known to have mean $2.3\text{ m}$. A scientist believes that, on average, trees of this age and variety in her region are slightly taller than in other places.

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• Question 4Oct/Nov 2023, paper 62Structured5 marks

  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 than 4.23, the heights of a random sample of 200 trees are measured.

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• Question 2May/June 2026, paper 63Structured6 marks

  Bettie believes that 30% of students at her school are vegetarian. Amir claims that the proportion is less than 30%. In order to test his claim, Amir takes a random sample of 20 students at the school.

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• Question 5May/June 2026, paper 63Structured14 marks

  The lengths, $X\text{ cm}$, of Wamba snakes have mean $\mu \text{ cm}$. Research has shown that, for the whole population of Wamba snakes, $\mu =41.5$. A researcher claims that, for the Wamba snakes in a particular region, the mean length is less than 41.5.

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• Question 3May/June 2025, paper 61Structured8 marks

  The time, $T$ minutes, for a certain daily bus journey is normally distributed. The bus company claims that the mean of $T$ is 45. A passenger believes that the mean of $T$ is actually greater than 45.

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• Question 4May/June 2024, paper 61Structured9 marks

  A random sample of 8 boxes of cereal from a certain supplier was taken. Each box was weighed and the masses in grams were as follows. 261 249 259 252 255 256 258 254 Find unbiased estimates of the population mean and variance.

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• Question 3May/June 2023, paper 61Structured6 marks

  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.

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• Question 6May/June 2025, paper 61Structured7 marks

  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 than 25%. He plans to test the manufacturer's claim.

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• Question 7May/June 2024, paper 61Structured11 marks

  Every July, as part of a research project, Rita collects data about sightings of a particular kind of bird. Each day in July she notes whether she sees this kind of bird or not, and she records the number $X$ of days on which she sees it.

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• Question 7May/June 2023, paper 61Structured14 marks

  The number of accidents per week at a certain factory has a Poisson distribution. In the past the mean has been 1.9 accidents per week. Last year, the manager gave all his employees a new booklet on safety.

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• Question 5May/June 2025, paper 62Structured4 marks

  The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable $X\sim \text{N}(\mu ,{\sigma }^2)$. In the past, the values of $\mu$ and $\sigma$ were 10.5 and 3.8 respectively.

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• Question 6May/June 2024, paper 62Structured10 marks

  The masses of cereal boxes filled by a certain machine have mean 510 grams. An adjustment is made to the machine and an inspector wishes to test whether the mean mass of cereal boxes filled by the machine has decreased.

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• Question 3May/June 2023, paper 62Structured8 marks

  The masses, in kilograms, of newborn babies in country $A$ are represented by the random variable $X$, with mean $\mu$ and variance ${\sigma }^2$. The masses of a random sample of 500 newborn babies in this country were found and the results are summarised below.

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• Question 8May/June 2025, paper 62Structured10 marks

  Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, $p$, that it will show a six on one throw is less than $\frac{1}{6}$.

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• Question 4May/June 2024, paper 63Structured5 marks

  In this question you should not use an approximating distribution. At an election in Menham last year, 24% of voters supported the Today Party. A student wishes to test whether support for the Today Party has decreased since last year.

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• Question 6May/June 2023, paper 62Structured5 marks

  When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randomly chosen child who completes a Mathlit will be awarded a medal is $\frac{1}{3}$. Asha wishes to test this claim.

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