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Date November 2017 Marks available 1 Reference code 17N.1.SL.TZ0.T_5
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Question number T_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 = 0.22 a + 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

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

0.22 ( 50 ) + 15     (M1)

 

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

 

( = )   26     (A1)     (C2)

OR

655 25     (M1)

 

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

 

( = )   26.2     (A1)     (C2)

[2 marks]

a.

line through ( 50 ,   26 ± 1 ) and ( 0 ,   15 )     (A1)(ft)(A1)     (C2)

 

Note: Award (A1)(ft) for a straight line through (50, their h ¯ ), and (A1) for the line intercepting the y -axis at ( 0 ,   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—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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