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Date November 2017 Marks available 2 Reference code 17N.1.sl.TZ0.5
Level SL only Paper 1 Time zone TZ0
Command term Draw Question number 5 Adapted from N/A

Question

A survey was carried out to investigate the relationship between a person’s age in years ( \(a\)) and the number of hours they watch television per week (\(h\)). The scatter diagram represents the results of the survey.

N17/5/MATSD/SP1/ENG/TZ0/05

The mean age of the people surveyed was 50.

For these results, the equation of the regression line \(h\) on \(a\) is \(h = 0.22a + 15\).

Find the mean number of hours that the people surveyed watch television per week.

[2]
a.

Draw the regression line on the scatter diagram.

[2]
b.

By placing a tick (✔) in the correct box, determine which of the following statements is true:

N17/5/MATSD/SP1/ENG/TZ0/05.c

[1]
c.

Diogo is 18 years old. Give a reason why the regression line should not be used to estimate the number of hours Diogo watches television per week.

[1]
d.

Markscheme

\(0.22(50) + 15\)     (M1)

 

Note:     Award (M1) for correct substitution of 50 into equation of the regression line.

 

\(( = ){\text{ }}26\)     (A1)     (C2)

OR

\(\frac{{655}}{{25}}\)     (M1)

 

Note:     Award (M1) for correctly summing the \(h\) values of the points, and dividing by 25.

 

\(( = ){\text{ }}26.2\)     (A1)     (C2)

[2 marks]

a.

line through \((50,{\text{ }}26 \pm 1)\) and \((0,{\text{ }}15)\)     (A1)(ft)(A1)     (C2)

 

Note: Award (A1)(ft) for a straight line through (50, their \(\bar h\)), and (A1) for the line intercepting the \(y\)-axis at \((0,{\text{ }}15)\); this may need to be extrapolated. Follow through from part (a). Award at most (A0)(A1) if the line is not drawn with a ruler.

 

[2 marks]

b.

N17/5/MATSD/SP1/ENG/TZ0/05.c/M     (A1) (C1)

 

Note:     Award (A0) if more than one tick (✔) is seen.

 

[1 mark]

c.

18 is less than the lowest age in the survey OR extrapolation.     (A1)     (C1)

 

Note:     Accept equivalent statements.

 

[1 mark]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 4 - Statistical applications » 4.3 » The regression line for \(y \) on \(x \).
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