surname names
Number Number
■ ■
Further Mathematics
Advanced
PAPER 4B: Further Statistics 2
Candidates may use any calculator permitted 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
• 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.
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.
• There are 8 questions in this question paper. The total mark for this paper is 75. – use this as a guide
as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. Two students are experimenting with some water in a plastic bottle. The bottle is filled with water
and a hole is put in the bottom of the bottle. The students record the time,
t seconds, it takes for the water level to fall to each of 10 given values of the height,
h cm, above the hole.
Student A models the data with an equation of the form t = a + b h
The data is coded using v = t – 40 and w = h and the following information is
obtained.
v 626 v2 64678 w 22.47 Sww 4.52 S 338.83
vw
(a) Find the equation of the regression line of t on h in the form t = a + b h
(4)
The time it takes the water level to fall to a height of 9 cm above the hole is 47 seconds.
(b) Calculate the residual for this data point.
Give your answer to 2 decimal places.
(2)
Given that the residual sum of squares (RSS) for the model of t on h is the same as
the RSS for the model of v on w,
(c) calculate the RSS for these 10 data points.
(2)
Student B models the data with an equation of the form t = c + dh
The regression line of t on h is calculated and the residual sum of squares (RSS) is found to be
980 to 3 significant figures.
(d) With reference to part (c) state, giving a reason, whether Student B‟s model or Student
A‟s model is the more suitable for these data.
(1)
,Question 1 continued
, Question 1 continued
Number Number
■ ■
Further Mathematics
Advanced
PAPER 4B: Further Statistics 2
Candidates may use any calculator permitted 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
• 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.
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.
• There are 8 questions in this question paper. The total mark for this paper is 75. – use this as a guide
as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. Two students are experimenting with some water in a plastic bottle. The bottle is filled with water
and a hole is put in the bottom of the bottle. The students record the time,
t seconds, it takes for the water level to fall to each of 10 given values of the height,
h cm, above the hole.
Student A models the data with an equation of the form t = a + b h
The data is coded using v = t – 40 and w = h and the following information is
obtained.
v 626 v2 64678 w 22.47 Sww 4.52 S 338.83
vw
(a) Find the equation of the regression line of t on h in the form t = a + b h
(4)
The time it takes the water level to fall to a height of 9 cm above the hole is 47 seconds.
(b) Calculate the residual for this data point.
Give your answer to 2 decimal places.
(2)
Given that the residual sum of squares (RSS) for the model of t on h is the same as
the RSS for the model of v on w,
(c) calculate the RSS for these 10 data points.
(2)
Student B models the data with an equation of the form t = c + dh
The regression line of t on h is calculated and the residual sum of squares (RSS) is found to be
980 to 3 significant figures.
(d) With reference to part (c) state, giving a reason, whether Student B‟s model or Student
A‟s model is the more suitable for these data.
(1)
,Question 1 continued
, Question 1 continued
