Candidate surname Other names
Centre Number Candidate Number
Paper
Statistics
� �
Advanced
PAPER 3 : Statistics in Practice
Marks
Statistical formulae and tables booklet
Calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have retrievable mathematical formulae stored in them.
Instructions
• Use black ink or ball‑point pen.
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
•
A booklet ‘Statistical formulae and tables’ is provided.
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.
• Ifand
Check your answers
you change if youabout
your mind havean
any working underneath.
time at thecross
answer, end. it out and put your new answer
Turn over
,BLANK PAGE
, Answer ALL questions. Write your answers in the spaces provided.
1 A study in 2021 investigated the number of hail days in a large European area covering
Germany, France, Belgium and Luxembourg
A hail day was defined as one in which a radar detected the conditions necessary for
hail to occur anywhere within this area. Over the past 20 years, the mean number of
hail days in a year in this area was 86
[Source : www.doi.org/10.5194/nhess‑21‑683‑2021]
(a) Find the probability that
(i) in a randomly chosen year there would be at least 90 hail days,
(2)
(ii) in a randomly chosen two‑year period, there are no more than 160 hail days.
(2)
(b) State two assumptions needed, in the context of this question, to calculate the
probabilities in (a) and in each case give a reason why that assumption may not
be appropriate.
(4)
(Total for Question 1 is 8 marks)
3
■■■■ Turn over
, 2 A small company based in the tourism industry is trying to decide where best to spend
its advertising budget in order to attract more visitors.
It is comparing the visitor numbers to mainland UK from France and from Ireland in
different periods of time.
Figure 1 shows the number of visitors from France and from Ireland for a randomly
selected series of yearly quarters. Visitor numbers have been rounded to the
nearest 1000
Quarter
2019 Q2 2019 Q3 2021 Q1 2021 Q3 2022 Q1 2022 Q3 2022 Q4
France 929 000 898 000 13 000 148 000 462 000 697 000 842 000
Country
Ireland 718 000 716 000 24 000 247 000 417 000 640 000 731 000
Figure 1
[Source : www.ons.gov.uk/peoplepopulationandcommunity/leisureandtourism]
In some quarters, the number of visitors from France exceeds that from Ireland, whilst
in others the reverse is true. The data is also clearly impacted by changes in travel
patterns following the pandemic.
You should assume that the difference between the numbers of visitors from France and
Ireland is not symmetrically distributed.
(a) Carry out a suitable hypothesis test to determine whether there is a difference
between the average number of visitors to mainland UK from the two countries.
(6)
4
■■■■
Centre Number Candidate Number
Paper
Statistics
� �
Advanced
PAPER 3 : Statistics in Practice
Marks
Statistical formulae and tables booklet
Calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have retrievable mathematical formulae stored in them.
Instructions
• Use black ink or ball‑point pen.
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
•
A booklet ‘Statistical formulae and tables’ is provided.
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.
• Ifand
Check your answers
you change if youabout
your mind havean
any working underneath.
time at thecross
answer, end. it out and put your new answer
Turn over
,BLANK PAGE
, Answer ALL questions. Write your answers in the spaces provided.
1 A study in 2021 investigated the number of hail days in a large European area covering
Germany, France, Belgium and Luxembourg
A hail day was defined as one in which a radar detected the conditions necessary for
hail to occur anywhere within this area. Over the past 20 years, the mean number of
hail days in a year in this area was 86
[Source : www.doi.org/10.5194/nhess‑21‑683‑2021]
(a) Find the probability that
(i) in a randomly chosen year there would be at least 90 hail days,
(2)
(ii) in a randomly chosen two‑year period, there are no more than 160 hail days.
(2)
(b) State two assumptions needed, in the context of this question, to calculate the
probabilities in (a) and in each case give a reason why that assumption may not
be appropriate.
(4)
(Total for Question 1 is 8 marks)
3
■■■■ Turn over
, 2 A small company based in the tourism industry is trying to decide where best to spend
its advertising budget in order to attract more visitors.
It is comparing the visitor numbers to mainland UK from France and from Ireland in
different periods of time.
Figure 1 shows the number of visitors from France and from Ireland for a randomly
selected series of yearly quarters. Visitor numbers have been rounded to the
nearest 1000
Quarter
2019 Q2 2019 Q3 2021 Q1 2021 Q3 2022 Q1 2022 Q3 2022 Q4
France 929 000 898 000 13 000 148 000 462 000 697 000 842 000
Country
Ireland 718 000 716 000 24 000 247 000 417 000 640 000 731 000
Figure 1
[Source : www.ons.gov.uk/peoplepopulationandcommunity/leisureandtourism]
In some quarters, the number of visitors from France exceeds that from Ireland, whilst
in others the reverse is true. The data is also clearly impacted by changes in travel
patterns following the pandemic.
You should assume that the difference between the numbers of visitors from France and
Ireland is not symmetrically distributed.
(a) Carry out a suitable hypothesis test to determine whether there is a difference
between the average number of visitors to mainland UK from the two countries.
(6)
4
■■■■
