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Date May Example questions Marks available 2 Reference code EXM.2.SL.TZ0.1
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Calculate Question number 1 Adapted from N/A

Question

The principal of a high school is concerned about the effect social media use might be having on the self-esteem of her students. She decides to survey a random sample of 9 students to gather some data. She wants the number of students in each grade in the sample to be, as far as possible, in the same proportion as the number of students in each grade in the school.

The number of students in each grade in the school is shown in table.

In order to select the 3 students from grade 12, the principal lists their names in alphabetical order and selects the 28th, 56th and 84th student on the list.

Once the principal has obtained the names of the 9 students in the random sample, she surveys each student to find out how long they used social media the previous day and measures their self-esteem using the Rosenberg scale. The Rosenberg scale is a number between 10 and 40, where a high number represents high self-esteem.

State the name for this type of sampling technique.

[1]
a.

Show that 3 students will be selected from grade 12.

[3]
b.i.

Calculate the number of students in each grade in the sample.

[2]
b.ii.

State the name for this type of sampling technique.

[1]
c.

Calculate Pearson’s product moment correlation coefficient, r .

[2]
d.i.

Interpret the meaning of the value of r  in the context of the principal’s concerns.

[1]
d.ii.

Explain why the value of r  makes it appropriate to find the equation of a regression line.

[1]
d.iii.

Another student at the school, Jasmine, has a self-esteem value of 29.            

By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.

[4]
e.

Markscheme

Stratified sampling          A1

[1 mark]

a.

There are 260 students in total         A1

84 260 × 9 = 2.91          M1A1

So 3 students will be selected.         AG

[3 marks]

b.i.

grade 9  = 60 260 × 9 2 ,  grade 10 = 83 260 × 9 3 ,  grade 11 = 33 260 × 9 1          A2

[2 marks]

b.ii.

Systematic sampling        A1

[1 mark]

c.

r = 0.901       A2

[2 marks]

d.i.

The negative value of r  indicates that more time spent on social media leads to lower self-esteem, supporting the principal’s concerns.      R1

[1 mark]

d.ii.

r being close to –1 indicates there is strong correlation, so a regression line is appropriate.      R1

[1 mark]

d.iii.

Find the regression line of t  on s .       M1

t = 0.281 s + 9.74         A1

t = ( 0.2807 ) ( 29 ) + 9.739 = 1.60 hours       M1A1

[4 marks]

e.

Examiners report

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a.
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b.i.
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b.ii.
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c.
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d.i.
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d.ii.
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d.iii.
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e.

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques
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Topic 4—Statistics and probability » SL 4.10—X on y regression line
Topic 4—Statistics and probability

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