21N.2.SL.TZ0.1

pestleMathematicsAASLPaper 221N· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

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]

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]

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]

Markscheme / solution

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]

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

$a = 1.37, b = 64.5$ A1

[1 mark]

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]

Examiners’ report

[N/A]