surname names
Number Number
Paper
Statistics
� �
Advanced
PAPER 2: Statistical Inference
Calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
Unless otherwise stated, inexact answers should be given to three
significant figures.
Unless otherwise stated, statistical tests should be carried out at the
5% significance level.
• There are 6 questions in this question paper. The total mark for this paper is 80.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
• Ifanyyouworking
change your mind about an answer, cross it out and put your new answer and
underneath.
Turn over
, Answer ALL questions. Write your answers in the spaces provided.
1 Since 2006 the RAC, a roadside assistance organisation, have used the RAC Pothole
Index to monitor the state of UK roads.
The Index is a measure of how often, on average, an RAC member requests roadside
assistance for a breakdown where damage from a pothole or other road surface defect
was most likely the cause of the breakdown.
An Index of 1.2 would mean the likelihood of pothole damage had increased by 20%
compared to 2006
A reporter sees that the most recently reported figure was 2.0 and wishes to write an
article about the likelihood of pothole damage, which she claims is now twice as great
as in 2006
[Source: How to report a pothole and claim for damage online | RAC Drive]
(a) Explain why the reporter is correct in her interpretation of the value of 2.0
(1)
For the years 2014 to 2021, the Pothole Index for each quarter was recorded, the
summary statistics are shown below.
x 70.05 x x 6.5596 n 32
2
(b) Test to see whether, on average, this evidence would have supported the reporter’s
claim between 2014 and 2021
(8)
2
■■■■
,Question 1 continued
(Total for Question 1 is 9 marks)
3
■■■■ Turn over
, 2 In the game of tennis, players score points in a number of ways.
An ace is a tennis stroke in which a player beginning the point strikes the ball so that
their opponent is unable to make contact with the ball. This wins the point for the player
beginning the point.
Daniil, a TV commentator, believes that the number of aces has begun to decrease over
recent years.
He collected data from a website for the total number of aces for each of the top
10 male professionals for the 2018 and 2023 French Open tournaments.
This is shown in Figure 1
2018 Number of Aces 2023 Number of Aces
12 10
14 19
27 20
37 27
40 32
44 36
47 42
55 43
57 45
76 50
Figure 1
[Source: Infosys Slam Leaderboard – Roland-Garros – The 2018/23 Roland-Garros Tournament
official site (rolandgarros.com)]
(a) Conduct a suitable distribution free test to investigate Daniil’s belief.
(9)
4
■■■■
Number Number
Paper
Statistics
� �
Advanced
PAPER 2: Statistical Inference
Calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear.
Answers without working may not gain full credit.
Unless otherwise stated, inexact answers should be given to three
significant figures.
Unless otherwise stated, statistical tests should be carried out at the
5% significance level.
• There are 6 questions in this question paper. The total mark for this paper is 80.
– use this as a guide as to how much time to spend on each question.
Advice
Read each question carefully before you start to answer it.
• Ifanyyouworking
change your mind about an answer, cross it out and put your new answer and
underneath.
Turn over
, Answer ALL questions. Write your answers in the spaces provided.
1 Since 2006 the RAC, a roadside assistance organisation, have used the RAC Pothole
Index to monitor the state of UK roads.
The Index is a measure of how often, on average, an RAC member requests roadside
assistance for a breakdown where damage from a pothole or other road surface defect
was most likely the cause of the breakdown.
An Index of 1.2 would mean the likelihood of pothole damage had increased by 20%
compared to 2006
A reporter sees that the most recently reported figure was 2.0 and wishes to write an
article about the likelihood of pothole damage, which she claims is now twice as great
as in 2006
[Source: How to report a pothole and claim for damage online | RAC Drive]
(a) Explain why the reporter is correct in her interpretation of the value of 2.0
(1)
For the years 2014 to 2021, the Pothole Index for each quarter was recorded, the
summary statistics are shown below.
x 70.05 x x 6.5596 n 32
2
(b) Test to see whether, on average, this evidence would have supported the reporter’s
claim between 2014 and 2021
(8)
2
■■■■
,Question 1 continued
(Total for Question 1 is 9 marks)
3
■■■■ Turn over
, 2 In the game of tennis, players score points in a number of ways.
An ace is a tennis stroke in which a player beginning the point strikes the ball so that
their opponent is unable to make contact with the ball. This wins the point for the player
beginning the point.
Daniil, a TV commentator, believes that the number of aces has begun to decrease over
recent years.
He collected data from a website for the total number of aces for each of the top
10 male professionals for the 2018 and 2023 French Open tournaments.
This is shown in Figure 1
2018 Number of Aces 2023 Number of Aces
12 10
14 19
27 20
37 27
40 32
44 36
47 42
55 43
57 45
76 50
Figure 1
[Source: Infosys Slam Leaderboard – Roland-Garros – The 2018/23 Roland-Garros Tournament
official site (rolandgarros.com)]
(a) Conduct a suitable distribution free test to investigate Daniil’s belief.
(9)
4
■■■■
