User interface language: English | Español

Date November 2021 Marks available 2 Reference code 21N.2.AHL.TZ0.1
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Determine 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=ah+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

r=0.884                         A1


Note:
Award the (M1) for any correct value of r, a, b or r2=0.780624 seen in part (a) or part (b).


[2 marks]

a.

a=1.36609 , b=64.5171

a=1.37 , b=64.5                       A1



[1 mark]

b.

attempt to find their difference                       (M1)

5×1.36609  OR  1.36609h+5+64.5171-1.36609h+64.5171

6.83045

=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
Show 120 related questions
Topic 4—Statistics and probability

View options