Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 16 May 2025
Afternoon Paper
reference 8FM0/23
Further Mathematics
Advanced Subsidiary
Further Mathematics options
23: Further Statistics 1
(Part of options B, E, F and G)
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or 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).
Fill in the boxes at the top of this page with your name,
••
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.
Values from statistical tables should be quoted in full. If a calculator is used instead of
•
tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
The total mark for this part of the examination is 40. There are 4 questions.
The marks for each question are shown in brackets
– 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.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P76372A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P76372A0116*
,1. A researcher is investigating the relationship between a person’s age and their preferred
method of shopping.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
A random sample of 300 people is taken and the results are summarised in the
table below.
Preferred method of shopping
Online In-store Total
18 – 30 27 23 50
31 – 50 31 59 90
Age
51 – 64 17 43 60
65 and older 30 70 100
Total 105 195 300
(a) Write down suitable hypotheses for a test to determine whether or not there is
evidence of an association between age and preferred method of shopping.
(1)
The researcher assumes that the null hypothesis is true and uses the data in the table to
find expected values.
(b) (i) Identify the cell which would have the smallest expected value.
(ii) Calculate the expected value for this cell.
(2)
O E
2
The value of
E
for the other 7 cells is 5.060
(c) Test, at the 5% level of significance, whether or not there is evidence of an
association between age and preferred method of shopping.
You should state the test statistic, degrees of freedom, critical value and
conclusion clearly.
(5)
(d) Explain whether or not your conclusion to part (c) would be the same if the test was
carried out at a 1% level of significance.
(2)
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2
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, Question 1 continued
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*P76372A0316* Turn over
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 16 May 2025
Afternoon Paper
reference 8FM0/23
Further Mathematics
Advanced Subsidiary
Further Mathematics options
23: Further Statistics 1
(Part of options B, E, F and G)
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or 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).
Fill in the boxes at the top of this page with your name,
••
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.
Values from statistical tables should be quoted in full. If a calculator is used instead of
•
tables the value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
The total mark for this part of the examination is 40. There are 4 questions.
The marks for each question are shown in brackets
– 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.
•
Try to answer every question.
Check your answers if you have time at the end.
Turn over
P76372A
©2025 Pearson Education Ltd.
Y:1/1/1/
*P76372A0116*
,1. A researcher is investigating the relationship between a person’s age and their preferred
method of shopping.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
A random sample of 300 people is taken and the results are summarised in the
table below.
Preferred method of shopping
Online In-store Total
18 – 30 27 23 50
31 – 50 31 59 90
Age
51 – 64 17 43 60
65 and older 30 70 100
Total 105 195 300
(a) Write down suitable hypotheses for a test to determine whether or not there is
evidence of an association between age and preferred method of shopping.
(1)
The researcher assumes that the null hypothesis is true and uses the data in the table to
find expected values.
(b) (i) Identify the cell which would have the smallest expected value.
(ii) Calculate the expected value for this cell.
(2)
O E
2
The value of
E
for the other 7 cells is 5.060
(c) Test, at the 5% level of significance, whether or not there is evidence of an
association between age and preferred method of shopping.
You should state the test statistic, degrees of freedom, critical value and
conclusion clearly.
(5)
(d) Explain whether or not your conclusion to part (c) would be the same if the test was
carried out at a 1% level of significance.
(2)
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P76372A0216*
, Question 1 continued
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DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
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3
*P76372A0316* Turn over
