Type I and Type II errors and power: AQA A‑Level Further Maths questions

AQA A-Level Further Maths past-paper questions on SC.1 Type I and Type II errors and power, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 15 questions on Type I and Type II errors and power, as a list

June 2025, Paper 3 Statistics, Q3 (1 mark): Cosmo is carrying out a hypothesis test. He rejects the null hypothesis. State which of the following statements is correct. Tick () one box. [1 mark] He could
June 2025, AS Paper 2 Statistics, Q7 (8 marks): Kristi set up a website for her new home business. The number of visitors per hour to the website is modelled using a Poisson distribution. During the first mon
June 2024, Paper 3 Statistics, Q10 (7 marks): The length, X cm, of teeth for an extinct breed of shark is known to have a normal distribution. A random sample of 250 teeth has the following summary statisti
June 2024, AS Paper 2 Statistics, Q7 (11 marks): Over a period of time, it has been shown that the mean number of customers entering a small store is 6 per hour. The store runs a promotion, selling many produc
June 2023, Paper 3 Statistics, Q7 (11 marks): Company A uses a machine to produce toys. The number of toys in a week that do not pass Company A’s quality checks is modelled by a Poisson distribution X with
June 2023, AS Paper 2 Statistics, Q4 (4 marks): The proportion, p, of people in a particular town who use the local supermarket is unknown. A random sample of 30 people in the town is taken and each person is
June 2022, AS Paper 2 Statistics, Q6 (8 marks): The number of computers sold per day by a shop can be modelled by the random variable Y where Y × Po(42) 6 (a) State the variance of Y [1 mark] 6 (b) One month
November 2021, Paper 3 Statistics, Q8 (13 marks): A company records the number of complaints, X, that it receives over 60 months. The summarised results are X x = 102 and X (x × x)2 = 103:25 8 (a) Using this da
November 2021, AS Paper 2 Statistics, Q4 (6 marks): The distance a particular football player runs in a match is modelled by a normal distribution with standard deviation 0.3 kilometres. A random sample of n matc
November 2020, Paper 3 Statistics, Q2 (1 mark): Jamie is conducting a hypothesis test on a random variable which has a normal distribution with standard deviation 1 The hypotheses are H0 : m = 5 H1 : m > 5 He
November 2020, Paper 3 Statistics, Q5 (7 marks): Emily claims that the average number of runners per minute passing a shop during a long distance run is 8 Emily conducts a hypothesis test to investigate her cl
November 2020, Paper 3 Statistics, Q7 (8 marks): The rainfall per day in February in a particular town has been recorded as having a mean of 1.8 inches. Sienna claims that rainfall in February has increased in
November 2020, AS Paper 2 Statistics, Q8 (9 marks): There are two hospitals in a city. Over a period of time, the first hospital recorded an average of 20 births a day. Over the same period of time, the second ho
June 2019, Paper 3 Statistics, Q2 (1 mark): Amy takes a sample of size 50 from a normal distribution with mean m and variance 16 She conducts a hypothesis test with hypotheses: H0 : m = 52 H1 : m > 52 She
June 2019, AS Paper 2 Statistics, Q2 (1 mark): A binomial hypothesis test was carried out at the 5% level of significance with the hypotheses H0 : p = 0:6 H1 : p > 0:6 A sample of size 30 was used to carry o

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