surname names
Number Number
Afternoon
🟐 🟐
Advanced Subsidiary
Further Mathematics options
23: Further Statistics 1
(Part of options B, E, F and G)
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
there may in thethan
be more space spaces
youprovided
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. – use this as a guide as to how
The marks
much timefor each question
to spend are shown in brackets
on each question.
Advice
• Edexcel As level further Mathematics Question Paper Option 23 June+
Read each question carefully before you start to answer it.
•
\
2025 Pearson Try to answer every question.
Mark scheme
,1. A researcher is investigating the relationship between a person’s age and their preferred
method of shopping.
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
DO NOT WRITE IN THIS AREA
(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
DO NOT WRITE IN THIS AREA
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)
2
■■■■
,
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
3
Turn over
Number Number
Afternoon
🟐 🟐
Advanced Subsidiary
Further Mathematics options
23: Further Statistics 1
(Part of options B, E, F and G)
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
there may in thethan
be more space spaces
youprovided
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. – use this as a guide as to how
The marks
much timefor each question
to spend are shown in brackets
on each question.
Advice
• Edexcel As level further Mathematics Question Paper Option 23 June+
Read each question carefully before you start to answer it.
•
\
2025 Pearson Try to answer every question.
Mark scheme
,1. A researcher is investigating the relationship between a person’s age and their preferred
method of shopping.
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
DO NOT WRITE IN THIS AREA
(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
DO NOT WRITE IN THIS AREA
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)
2
■■■■
,
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
■■■■
Question 1 continued
3
Turn over
