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Date	November 2021	Marks available	1	Reference code	21N.2.AHL.TZ0.1
Level	Additional Higher Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Comment	Question number	1	Adapted from	N/A

Question

In Lucy’s music academy, eight students took their piano diploma examination and achieved scores out of 150. For her records, Lucy decided to record the average number of hours per week each student reported practising in the weeks prior to their examination. These results are summarized in the table below.

Find Pearson’s product-moment correlation coefficient, $r$ , for these data.

[2]

a.

The relationship between the variables can be modelled by the regression equation $D = a h + b$ . Write down the value of $a$ and the value of $b$ .

[1]

b.

One of these eight students was disappointed with her result and wished she had practised more. Based on the given data, determine how her score could have been expected to alter had she practised an extra five hours per week.

[2]

c.

Lucy asserts that the number of hours a student practises has a direct effect on their final diploma result. Comment on the validity of Lucy’s assertion.

[1]

d.

Lucy suspected that each student had not been practising as much as they reported. In order to compensate for this, Lucy deducted a fixed number of hours per week from each of the students’ recorded hours.

State how, if at all, the value of $r$ would be affected.

[1]

e.

Markscheme

use of GDC to give (M1)

$r = 0.883529 \dots$

$r = 0.884$ A1

Note: Award the (M1) for any correct value of $r$ , $a$ , $b$ or $r^{2} = 0.780624 \dots$ seen in part (a) or part (b).

[2 marks]

a.

$a = 1.36609 \dots, b = 64.5171 \dots$

$a = 1.37, b = 64.5$ A1

[1 mark]

b.

attempt to find their difference (M1)

$5 \times 1.36609 \dots$ OR $1.36609 \dots (h + 5) + 64.5171 \dots - (1.36609 \dots h + 64.5171 \dots)$

$6.83045 \dots$

$= 6.83$ $(6.85 from 1.37)$

the student could have expected her score to increase by $7$ marks. A1

Note: Accept an increase of $6, 6.83$ or $6.85$ .

[2 marks]

c.

Lucy is incorrect in suggesting there is a causal relationship.

This might be true, but the data can only indicate a correlation. R1

Note: Accept ‘Lucy is incorrect as correlation does not imply causation’ or equivalent.

[1 mark]

d.

no effect A1

[1 mark]

e.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

[N/A]

e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x

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21N.2.SL.TZ0.1a:
Find Pearson’s product-moment correlation coefficient, $r$ , for these data.
21N.2.AHL.TZ0.1a:
Find Pearson’s product-moment correlation coefficient, $r$ , for these data.
21N.2.AHL.TZ0.1e:
Lucy suspected that each student had not been practising as much as they reported. In order to compensate for this, Lucy deducted a fixed number of hours per week from each of the students’ recorded hours.

State how, if at all, the value of $r$ would be affected.
17M.2.SL.TZ1.T_1a:
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17M.2.SL.TZ1.T_1c:
Write down the equation of the regression line $y$ on $x$ , in the form $y = mx + c$ .
17M.2.SL.TZ1.T_1d:
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17M.2.SL.TZ1.T_1e:
Find the percentage error in your estimate in part (d).
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State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.
18N.2.SL.TZ0.T_1c.ii:
Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.
18N.2.SL.TZ0.T_1d:
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Calculate the percentage error in Jerome’s estimated examination score.
16N.2.SL.TZ0.T_1a:
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16N.2.SL.TZ0.T_1b:
(i) ${\bar x}$ , the mean number of hours spent on social media;

(ii) ${\bar y}$ , the mean number of IB Diploma points.
16N.2.SL.TZ0.T_1f:
Draw the regression line, from part (e), on your scatter diagram.
16N.2.SL.TZ0.T_1g:
Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.
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17M.2.SL.TZ2.T_3g:
Draw the regression line $C$ on $x$ on the scatter diagram.
17M.2.SL.TZ2.T_3h:
Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.

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