Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Time 1 hour 30 minutes Paper
reference WST03/01
Mathematics
International Advanced Subsidiary/ Advanced Level
Statistics S3
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Yellow), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic 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 the statistical tables should be quoted in full. If a calculator is used instead of
•
the 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.
•
There are 7 questions in this question paper. The total mark for this paper is 75.
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.
If you change your mind about an answer, cross it out and put your new
answer and any working underneath.
Turn over
P72906A
©2023 Pearson Education Ltd.
J:1/1/1/1/1/
*P72906A0128*
,1 A machine fills bottles with mineral water.
The machine is checked every day to ensure that it is working correctly. On a particular
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
day a random sample of 100 bottles is taken. The volume of water, x millilitres, for each
bottle is measured and each measurement is coded using
y x
1000
The results are summarised below
y 847
y 2 13 510.09
(a) (i) Show that the value of the unbiased estimate of the mean of x is 1008.47
(ii) Calculate the unbiased estimate of the variance of x
(4)
The machine was initially set so that the volume of water in a bottle had a mean value
of 1010 millilitres.
Later, a test at the 5% significance level is used to determine whether or not the mean
volume of water in a bottle has changed. If it has changed then the machine is stopped
and reset.
(b) Write down suitable null and alternative hypotheses for a 2-tailed test.
(1)
(c) Find the critical region for X in the above test.
(4)
(d) Using your answer to part (a) and your critical region found in part (c), comment on
whether or not the machine needs to be stopped and reset.
Give a reason for your answer.
(2)
(e) Explain why the use of σ 2 s 2 is reasonable in this situation.
(1)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P72906A0228*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3
*P72906A0328* Turn over
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel International Advanced Level
Time 1 hour 30 minutes Paper
reference WST03/01
Mathematics
International Advanced Subsidiary/ Advanced Level
Statistics S3
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Yellow), calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic 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 the statistical tables should be quoted in full. If a calculator is used instead of
•
the 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.
•
There are 7 questions in this question paper. The total mark for this paper is 75.
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.
If you change your mind about an answer, cross it out and put your new
answer and any working underneath.
Turn over
P72906A
©2023 Pearson Education Ltd.
J:1/1/1/1/1/
*P72906A0128*
,1 A machine fills bottles with mineral water.
The machine is checked every day to ensure that it is working correctly. On a particular
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
day a random sample of 100 bottles is taken. The volume of water, x millilitres, for each
bottle is measured and each measurement is coded using
y x
1000
The results are summarised below
y 847
y 2 13 510.09
(a) (i) Show that the value of the unbiased estimate of the mean of x is 1008.47
(ii) Calculate the unbiased estimate of the variance of x
(4)
The machine was initially set so that the volume of water in a bottle had a mean value
of 1010 millilitres.
Later, a test at the 5% significance level is used to determine whether or not the mean
volume of water in a bottle has changed. If it has changed then the machine is stopped
and reset.
(b) Write down suitable null and alternative hypotheses for a 2-tailed test.
(1)
(c) Find the critical region for X in the above test.
(4)
(d) Using your answer to part (a) and your critical region found in part (c), comment on
whether or not the machine needs to be stopped and reset.
Give a reason for your answer.
(2)
(e) Explain why the use of σ 2 s 2 is reasonable in this situation.
(1)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2
*P72906A0228*
, Question 1 continued
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3
*P72906A0328* Turn over
