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Hypothesis testing

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 107

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 43 parts, 107 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · AS Paper 2 (Statistics) · Q3(b)(i) · 4 marks
Jayda believes that the true proportion of green counters in the bag is greater than 0.2 She takes a random sample of 40 counters from the bag, one at a time, with replacement. There are 11 green counters in her sample. (b) (i) Use a suitable test to assess Jayda’s belief. You should • state your hypotheses clearly • use a 5% level of significance • state the p‑value for the test (4)
2. June 2025 · AS Paper 2 (Statistics) · Q3(b)(ii) · 2 marks
(ii) Find the acceptance region for the test in part (i). (2)
3. June 2025 · Paper 3 (Statistics) · Q3(b) · 3 marks
Once every six months, the manufacturer tests whether the proportion of defective components has changed using hypotheses H0 : p = 0.015 and H1 : p ≠ 0.015 A random sample of 260 components is taken and 8 are found to be defective. (b) Using a 5% level of significance, complete the test. (3)
4. June 2025 · Paper 3 (Statistics) · Q4(e) · 2 marks
The teacher used all the data for these variables from the large data set for Leeming in 2015, as a sample. The teacher calculated the product moment correlation coefficient for x and y to be – 0.160 In a suitable test to determine whether there is evidence to support the teacher’s claim, the p-value was 0.015 (e) Using a 5% level of significance, state the hypotheses and conclusion for this test. (2)
5. June 2024 · AS Paper 2 (Statistics) · Q4(b) · 4 marks
Historical records show that the proportion of defective items produced by a machine is 0.12 Following a maintenance service of the machine, a random sample of 60 items is taken and 3 defective items are found. (b) Carry out a suitable test to determine whether the proportion of defective items produced by the machine has decreased following the maintenance service. You should state your hypotheses clearly and use a 5% level of significance. (4)
6. June 2024 · AS Paper 2 (Statistics) · Q4(c) · 1 marks
(c) Write down the p-value for your test in part (b) (1)
7. June 2024 · Paper 3 (Statistics) · Q2(b) · 3 marks
The product moment correlation coefficient between h and t is – 0.510 (b) Test whether or not there is evidence of a negative correlation between the height above the ground and the time during the flight. You should • state your hypotheses clearly • use a 5% level of significance • state the critical value used (3)
8. June 2024 · Paper 3 (Statistics) · Q4(a) · 4 marks
4. The proportion of left-handed adults in a country is 10% Freya believes that the proportion of left-handed adults under the age of 25 in this country is different from 10% She takes a random sample of 40 adults under the age of 25 from this country to investigate her belief. (a) Find the critical region for a suitable test to assess Freya’s belief. You should • state your hypotheses clearly • use a 5% level of significance • state the probability of rejection in each tail (4)
9. June 2024 · Paper 3 (Statistics) · Q4(b) · 1 marks
(b) Write down the actual significance level of your test in part (a) (1)
10. June 2024 · Paper 3 (Statistics) · Q4(c) · 1 marks
In Freya’s sample 7 adults were left-handed. (c) With reference to your answer in part (a) comment on Freya’s belief. (1)
11. June 2023 · AS Paper 2 (Statistics) · Q4(a) · 1 marks
4. Past information shows that 25% of adults in a large population have a particular allergy. Rylan believes that the proportion that has the allergy differs from 25% He takes a random sample of 50 adults from the population. Rylan carries out a test of the null hypothesis H0: p = 0.25 using a 5% level of significance. (a) Write down the alternative hypothesis for Rylan’s test. (1)
12. June 2023 · AS Paper 2 (Statistics) · Q4(b) · 4 marks
(b) Find the critical region for this test. You should state the probability associated with each tail, which should be as close to 2.5% as possible. (4)
13. June 2023 · AS Paper 2 (Statistics) · Q4(c) · 1 marks
(c) State the actual probability of incorrectly rejecting H0 for this test. (1)
14. June 2023 · AS Paper 2 (Statistics) · Q4(d) · 1 marks
Rylan finds that 10 of the adults in his sample have the allergy. (d) State the conclusion of Rylan’s hypothesis test. (1)
15. June 2023 · Paper 3 (Statistics) · Q2(d) · 4 marks
Kamil claims that the proportion of packets containing a prize is less than 1 A random sample of 110 packets is taken and 9 packets contain a prize. (d) Use a suitable test to assess Kamil’s claim. You should • state your hypotheses clearly • use a 5% level of significance (4)
16. June 2023 · Paper 3 (Statistics) · Q4(b) · 4 marks
A student claimed that the mean height of adult men from region B of this country was different from the mean height of adult men from region A. A random sample of 52 adult men from region B had a mean height of 177.2 cm The student assumed that the standard deviation of heights of adult men was 6.8 cm both for region A and region B. (b) Use a suitable test to assess the student’s claim. You should • state your hypotheses clearly • use a 5% level of significance (4)
17. June 2023 · Paper 3 (Statistics) · Q4(c) · 1 marks
(c) Find the p-value for the test in part (b) (1)
18. June 2022 · AS Paper 2 (Statistics) · Q2(b) · 4 marks
Supplier B claims that when it supplies bags of sugar, the proportion of bags that are damp is less than 8% The manufacturer takes a random sample of 70 bags of sugar from supplier B and finds that only 2 of the bags are damp. (b) Carry out a suitable test to assess supplier B’s claim. You should state your hypotheses clearly and use a 10% level of significance. (4)
19. June 2022 · Paper 3 (Statistics) · Q4(a) · 1 marks
4. A dentist knows from past records that 10% of customers arrive late for their appointment. A new manager believes that there has been a change in the proportion of customers who arrive late for their appointment. A random sample of 50 of the dentist's customers is taken. (a) Write down • a null hypothesis corresponding to no change in the proportion of customers who arrive late • an alternative hypothesis corresponding to the manager's belief (1)
20. June 2022 · Paper 3 (Statistics) · Q4(b) · 3 marks
(b) Using a 5% level of significance, find the critical region for a two-tailed test of the null hypothesis in (a) You should state the probability of rejection in each tail, which should be less than 0.025 (3)
21. June 2022 · Paper 3 (Statistics) · Q4(c) · 1 marks
(c) Find the actual level of significance of the test based on your critical region from part (b) (1)
22. June 2022 · Paper 3 (Statistics) · Q4(d) · 1 marks
The manager observes that 15 of the 50 customers arrived late for their appointment. (d) With reference to part (b), comment on the manager’s belief. (1)
23. June 2022 · Paper 3 (Statistics) · Q6(b) · 3 marks
Anna codes the data using the formulae x = log10 m y = log10 h The product moment correlation coefficient between x and y is – 0.897 (b) Test whether or not there is significant evidence of a negative correlation between x and y You should • state your hypotheses clearly • use a 5% level of significance • state the critical value used (3)
24. Oct 2021 · AS Paper 2 (Statistics) · Q4(d) · 4 marks
After several children have used beads from the sack, the nursery teacher decides to test whether or not the proportion of red beads in the sack has changed. She takes a random sample of 75 beads and finds 4 red beads. (d) Stating your hypotheses clearly, use a 5% significance level to carry out a suitable test for the teacher. (4)
25. Oct 2021 · AS Paper 2 (Statistics) · Q4(e) · 1 marks
(e) Find the p‑value in this case. (1)
26. Oct 2021 · Paper 3 (Statistics) · Q2(c) · 1 marks
The results from Marc’s random sample of 16 observations are given in the table below. x y (c) Use your calculator to find the product moment correlation coefficient between x and y for these data. (1)
27. Oct 2021 · Paper 3 (Statistics) · Q2(d) · 3 marks
(d) Test whether or not there is evidence of a negative correlation between the number of letters in the last name and the number of letters in the first name. You should • state your hypotheses clearly • use a 5% level of significance (3)
28. Oct 2021 · Paper 3 (Statistics) · Q5(d) · 4 marks
The heights of females from a different country are normally distributed with a standard deviation of 7.4 cm Mia believes that the mean height of females from this country is less than 166.5 cm Mia takes a random sample of 50 females from this country and finds the mean of her sample is 164.6 cm (d) Carry out a suitable test to assess Mia’s belief. You should • state your hypotheses clearly • use a 5% level of significance (4)
29. Oct 2020 · AS Paper 2 (Statistics) · Q5(c) · 4 marks
Rowan works in the same call centre as Afrika and believes he is a more successful salesperson. To check Rowan’s belief, Afrika monitors the next 35 sales calls Rowan makes and finds that 11 of the sales calls are successful. (c) Stating your hypotheses clearly test, at the 5% level of significance, whether or not there is evidence to support Rowan’s belief. (4)
30. Oct 2020 · Paper 3 (Statistics) · Q2(c) · 3 marks
Stav believes that there is a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity at Heathrow. He calculates the product moment correlation coefficient between these two variables for a random sample of 30 days and obtains r = -0.377 (c) Carry out a suitable test to investigate Stav’s belief at a 5% level of significance. State clearly ● your hypotheses ● your critical value (3)
31. Oct 2020 · Paper 3 (Statistics) · Q2(d) · 1 marks
On a random day at Heathrow the Daily Maximum Relative Humidity was 97% (d) Comment on the number of hours of sunshine you would expect on that day, giving a reason for your answer. (1)
32. Oct 2020 · Paper 3 (Statistics) · Q5(b) · 4 marks
Some patients complain that the mean time the doctor spends with a patient is more than 10 minutes. The receptionist takes a random sample of 20 patients and finds that the mean time the doctor spends with a patient is 11.5 minutes. (b) Stating your hypotheses clearly and using a 5% significance level, test whether or not there is evidence to support the patients’ complaint. (4)
33. June 2019 · AS Paper 2 (Statistics) · Q5(a) · 2 marks
5. Past records show that 15% of customers at a shop buy chocolate. The shopkeeper believes that moving the chocolate closer to the till will increase the proportion of customers buying chocolate. After moving the chocolate closer to the till, a random sample of 30 customers is taken and 8 of them are found to have bought chocolate. Julie carries out a hypothesis test, at the 5% level of significance, to test the shopkeeper’s belief. Julie’s hypothesis test is shown below. H0 : p = 0.15 H1 : p . 0.15 Let X = the number of customers who buy chocolate. X ~ B(30, 0.15) P(X = 8) = 0.0420 0.0420 : 0.05 so reject H0 There is sufficient evidence to suggest that the proportion of customers buying chocolate has increased. (a) Identify the first two errors that Julie has made in her hypothesis test. (2)
34. June 2019 · AS Paper 2 (Statistics) · Q5(b) · 1 marks
(b) Explain whether or not these errors will affect the conclusion of her hypothesis test. Give a reason for your answer. (1)
35. June 2019 · AS Paper 2 (Statistics) · Q5(c) · 2 marks
(c) Find, using a 5% level of significance, the critical region for a one-tailed test of the shopkeeper’s belief. The probability in the tail should be less than 0.05 (2)
36. June 2019 · AS Paper 2 (Statistics) · Q5(d) · 1 marks
(d) Find the actual level of significance of this test. (1)
37. June 2019 · Paper 3 (Statistics) · Q3(a) · 3 marks
3. Barbara is investigating the relationship between average income (GDP per capita), x US dollars, and average annual carbon dioxide (CO,) emissions, y tonnes, for different countries. She takes a random sample of 24 countries and finds the product moment correlation coefficient between average annual CO, emissions and average income to be 0.446 (a) Stating your hypotheses clearly, test, at the 5% level of significance, whether or not the product moment correlation coefficient for all countries is greater than zero. 3)
38. June 2019 · Paper 3 (Statistics) · Q3(b) · 1 marks
Barbara believes that a non-linear model would bea better fit to the data. She codes the data using the coding m = log,,x and c = log,,y and obtains the model c = -1.82 + 0.89m The product moment correlation coefficient between c and m is found to be 0.882 (b) Explain how this value supports Barbara’s belief. (1)
39. June 2019 · Paper 3 (Statistics) · Q5(c) · 5 marks
The machine is adjusted so that the standard deviation of the liquid put in the bottles is now 0.16ml Following the adjustments, Hannah believes that the mean amount of liquid put in each bottle is less than 25 ml She takes a random sample of 20 bottles and finds the mean amount of liquid to be 24.94 ml (c) Test Hannah’s belief at the 5% level of significance. You should state your hypotheses clearly. (5)
40. June 2018 · AS Paper 2 · Q3(b) · 4 marks
Naasir claims he has a method to help him win more than 1 3 of the games. To test this claim, the three of them played the game again 32 times and Naasir won 16 of these games. (b) Stating your hypotheses clearly, test Naasir’s claim at the 5% level of significance. (4)
41. June 2018 · Paper 3 · Q2(a) · 3 marks
2. Tessa owns a small clothes shop in a seaside town. She records the weekly sales figures, £ w, and the average weekly temperature, t °C, for 8 weeks during the summer. The product moment correlation coefficient for these data is -0.915 (a) Stating your hypotheses clearly and using a 5% level of significance, test whether or not the correlation between sales figures and average weekly temperature is negative. (3)
42. June 2018 · Paper 3 · Q2(c) · 1 marks
Tessa suggests that a linear regression model could be used to model these data. (c) State, giving a reason, whether or not the correlation coefficient is consistent with Tessa’s suggestion. (1)
43. June 2018 · Paper 3 · Q5(d) · 5 marks
After her exams, Alice believed that the lifetime of the batteries was more than 18 hours. She took a random sample of 20 of these batteries and found that their mean lifetime was 19.2 hours. (d) Stating your hypotheses clearly and using a 5% level of significance, test Alice’s belief. (5)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · AS Paper 2 (Statistics) · Q3
Mark scheme June 2025 Paper 2 (Statistics) Q3(b)(ii)
June 2025 · Paper 3 (Statistics) · Q3
Mark scheme June 2025 Paper 3 (Statistics) Q3(b)
June 2025 · Paper 3 (Statistics) · Q4
Mark scheme June 2025 Paper 3 (Statistics) Q4(e)
June 2024 · AS Paper 2 (Statistics) · Q4
Mark scheme June 2024 Paper 2 (Statistics) Q4(c)
June 2024 · Paper 3 (Statistics) · Q2
Mark scheme June 2024 Paper 3 (Statistics) Q2(b)
June 2024 · Paper 3 (Statistics) · Q4
Mark scheme June 2024 Paper 3 (Statistics) Q4(c)
June 2023 · AS Paper 2 (Statistics) · Q4
Mark scheme June 2023 Paper 2 (Statistics) Q4(d)
June 2023 · Paper 3 (Statistics) · Q2
Mark scheme June 2023 Paper 3 (Statistics) Q2(d)
June 2023 · Paper 3 (Statistics) · Q4
Mark scheme June 2023 Paper 3 (Statistics) Q4(c)
June 2022 · AS Paper 2 (Statistics) · Q2
Mark scheme June 2022 Paper 2 (Statistics) Q2(b)
June 2022 · Paper 3 (Statistics) · Q4
Mark scheme June 2022 Paper 3 (Statistics) Q4(d)
June 2022 · Paper 3 (Statistics) · Q6
Mark scheme June 2022 Paper 3 (Statistics) Q6(b)
Oct 2021 · AS Paper 2 (Statistics) · Q4
Mark scheme Oct 2021 Paper 2 (Statistics) Q4(e)
Oct 2021 · Paper 3 (Statistics) · Q2
Mark scheme Oct 2021 Paper 3 (Statistics) Q2(d)
Oct 2021 · Paper 3 (Statistics) · Q5
Mark scheme Oct 2021 Paper 3 (Statistics) Q5(d)
Oct 2020 · AS Paper 2 (Statistics) · Q5
Mark scheme Oct 2020 Paper 2 (Statistics) Q5(c)
Oct 2020 · Paper 3 (Statistics) · Q2
Mark scheme Oct 2020 Paper 3 (Statistics) Q2(d)
Oct 2020 · Paper 3 (Statistics) · Q5
Mark scheme Oct 2020 Paper 3 (Statistics) Q5(b)
June 2019 · AS Paper 2 (Statistics) · Q5
Mark scheme June 2019 Paper 2 (Statistics) Q5(d)
June 2019 · Paper 3 (Statistics) · Q3
Mark scheme June 2019 Paper 3 (Statistics) Q3(b)
June 2019 · Paper 3 (Statistics) · Q5
Mark scheme June 2019 Paper 3 (Statistics) Q5(c)
June 2018 · AS Paper 2 · Q3
Mark scheme June 2018 Paper 2 Q3(b)
June 2018 · Paper 3 · Q2
Mark scheme June 2018 Paper 3 Q2(c)
June 2018 · Paper 3 · Q5
Mark scheme June 2018 Paper 3 Q5(d)