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Date November 2020 Marks available 2 Reference code 20N.2.SL.TZ0.T_1
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Write down Question number T_1 Adapted from N/A

Question

Don took part in a project investigating wind speed, xkm h-1, and the time, y minutes, to fully charge a solar powered robot.

The investigation was carried out six times. The results are recorded in the table.

M is the point with coordinates (x, y).

On graph paper, draw a scatter diagram to show the results of Don’s investigation. Use a scale of 1cm to represent 2 units on the x-axis, and 1cm to represent 5 units on the y-axis.

[4]
a.

Calculate x, the mean wind speed.

[1]
b.i.

Calculate y, the mean time to fully charge the robot.

[1]
b.ii.

Plot and label the point M on your scatter diagram.

[2]
c.

Calculate r, Pearson’s product–moment correlation coefficient.

[2]
d.i.

Describe the correlation between the wind speed and the time to fully charge the robot.

[2]
d.ii.

Write down the equation of the regression line y on x, in the form y=mx+c.

[2]
e.i.

Draw this regression line on your scatter diagram.

[2]
e.ii.

Hence or otherwise estimate the charging time when the wind speed is 27km h-1.

[2]
e.iii.

Don concluded from his investigation: “There is no causation between wind speed and the time to fully charge the robot”.

In the context of the question, briefly explain the meaning of “no causation”.

[1]
f.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

       (A4)


Note:
Award (A1) for correct scales and labels.
Award (A3) for all six points correctly plotted.
Award (A2) for four or five points correctly plotted.
Award (A1) for two or three points correctly plotted.
Award at most (A0)(A3) if axes reversed.
If graph paper is not used, award at most (A1)(A0)(A0)(A0).


[4 marks]

a.

19km h-1       (A1)


[1 mark]

b.i.

32  (minutes)      (A1)


[1 mark]

b.ii.

point in correct position, labelled M     (A1)(ft)(A1)

Note: Award (A1)(ft) for point plotted in correct position, (A1) for point labelled M Follow through from their part (b).


[2 marks]

c.

r=   0.944  0.943733     (G2)

Note: Award (G1) for 0.943 (incorrect rounding).

[2 marks]

d.i.

(very) strong positive correlation   (A1)(ft)(A1)(ft)

Note: Award (A1)(ft) for (very) strong. Award (A1)(ft) for positive. Follow though from their part (d)(i). If there is no answer to part (d)(i), award at most (A0)(A1) for a correct direction.

[2 marks]

d.ii.

y=0.465x+23.2    y=0.465020x+23.1646   (A1)(A1)(G2)

Note: Award (A1) for 0.465x. Award (A1) for 23.2. If the answer is not an equation, award at most (A1)(A0).

[2 marks]

e.i.

regression line through their M        (A1)(ft)

regression line through their (0, 23.2)        (A1)(ft)

Note: Award a maximum of (A1)(A0) if the line is not straight/ruler not used. Award (A0)(A0) if the points are connected.
Follow through from their point M in part (b) and their y-intercept in part (e)(i).
If M is not plotted or labelled, then follow through from part (b).

[2 marks]

e.ii.

y= 0.46502027+23.1646        (M1)


Note:
 Award (M1) for correct substitution into their regression equation.


35.7 (minutes) 35.7201        (A1)(ft)(G2)


Note:
Follow through from their equation in part (e)(i).


OR

an attempt to use their regression line to find the y value at x=27


Note:
 Award (M1) for an indication of using their regression line. This must be illustrated by vertical and horizontal lines or marks at the correct place(s) on their scatter diagram.


35.7 (minutes)        (A1)(ft)


Note: Follow through from part (e)(ii).


[2 marks]

e.iii.

wind speed does not cause a change in the time to charge (the robot)      (A1)


Note:
 Award (A1) for a statement that communicates the meaning of a non-causal relationship between the two variables.


[1 mark]

f.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.
[N/A]
d.i.
[N/A]
d.ii.
[N/A]
e.i.
[N/A]
e.ii.
[N/A]
e.iii.
[N/A]
f.

Syllabus sections

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

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