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Date May 2011 Marks available 2 Reference code 11M.2.sl.TZ1.1
Level SL only Paper 2 Time zone TZ1
Command term Estimate Question number 1 Adapted from N/A

Question

The heat output in thermal units from burning 1 kg of wood changes according to the wood’s percentage moisture content. The moisture content and heat output of 10 blocks of the same type of wood each weighing 1 kg were measured. These are shown in the table.

Draw a scatter diagram to show the above data. Use a scale of 2 cm to represent 10% on the x-axis and a scale of 2 cm to represent 10 thermal units on the y-axis.

[4]
a.

Write down
(i)     the mean percentage moisture content, ˉx ;
(ii)    the mean heat output, ˉy .

[2]
b.

Plot the point (ˉxˉy) on your scatter diagram and label this point M .

[2]
c.

Write down the product-moment correlation coefficient, r .

[2]
d.

The equation of the regression line y on x is y=0.470x+83.7 . Draw the regression line y on x on your scatter diagram.

[2]
e.

The equation of the regression line y on x is y=0.470x+83.7 . Estimate the heat output in thermal units of a 1 kg block of wood that has 25% moisture content.

[2]
f.

The equation of the regression line y on x is y=0.470x+83.7 . State, with a reason, whether it is appropriate to use the regression line y on x to estimate the heat output in part (f).

[2]
g.

Markscheme

     (A1) for correct scales and labels
     (A3) for all ten points plotted correctly
     (A2) for eight or nine points plotted correctly
     (A1) for six or seven points plotted correctly     (A4)

 

Note: Award at most (A0)(A3) if axes reversed.

[4 marks]

a.

(i)     ˉx=42     (A1)


(ii)    ˉy=64     (A1)

 

[2 marks]

b.

(ˉxˉy) plotted on graph and labelled, M     (A1)(ft)(A1)

Note: Award (A1)(ft) for position, (A1) for label.

[2 marks]

c.

0.998    (G2)

Note: Award (G1) for correct sign, (G1) for correct absolute value.

[1 mark]

d.

line on graph (A1)(ft)(A1)

Notes: Award (A1)(ft) for line through their M, (A1) for approximately correct intercept (allow between 83 and 85). It is not necessary that the line is seen to intersect the y-axis. The line must be straight for any mark to be awarded.

[2 marks]

e.

y=0.470(25)+83.7     (M1)

Note: Award (M1) for substitution into formula or some indication of method on their graph. y=0.470(0.25)+83.7 is incorrect.

 

=72.0 (accept 71.95 and 72)     (A1)(ft)(G2)

Note: Follow through from graph only if they show working on their graph. Accept 72±0.5 .

[2 marks]

f.

Yes since 25% lies within the data set and r is close to 1     (R1)(A1)

Note: Accept Yes, since r is close to 1

Note: Do not award (R0)(A1).

[2 marks]

g.

Examiners report

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

a.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

b.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

c.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

d.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

e.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

f.

The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect scales being used; SI units are standard in this course and candidates are expected to know the difference between centimetres and millimetres (2) the lack of r on the GDC (3) not knowing that the regression line y on x passes through the mean point and (4) not realising that the value of r determines the validity of using the regression line y on x .

g.

Syllabus sections

Topic 4 - Statistical applications » 4.3 » Use of the regression line for prediction purposes.
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