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Date May 2017 Marks available 2 Reference code 17M.1.sl.TZ1.6
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 6 Adapted from N/A

Question

In a school, students in grades 9 to 12 were asked to select their preferred drink. The choices were milk, juice and water. The data obtained are organized in the following table.

M17/5/MATSD/SP1/ENG/TZ1/06

A χ2 test is carried out at the 5% significance level with hypotheses:

H0: the preferred drink is independent of the gradeH1: the preferred drink is not independent of the grade

The χ2 critical value for this test is 12.6.

Write down the value of x.

[1]
a.

Write down the number of degrees of freedom for this test.

[1]
b.

Use your graphic display calculator to find the χ2 statistic for this test.

[2]
c.

State the conclusion for this test. Give a reason for your answer.

[2]
d.

Markscheme

30     (A1)     (C1)

[1 mark]

a.

6     (A1)     (C1)

[1 mark]

b.

19.0 (18.9640)     (A2)(ft)     (C2)

 

Note:     Follow through from part (a).

Award (A1) for truncation to 18.9.

 

[2 marks]

c.

reject (do not accept) H0ORaccept H1     (A1)(ft)

 

Note:     Can be written in words.

 

19.0 (18.9640)>12.6     (R1)     (C2)

 

Note:     Accept “χ2calc>χ2crit” for the (R1) provided their χ2calc value is explicitly seen in their part (c).

 

OR

(p=) 0.00422 <(significance level  = ) 0.05     (R1)     (C2)

 

Note:     Do not award (R0)(A1)(ft). Follow through from part (c). Numerical comparison must be seen to award the (R1).

 

[2 marks]

d.

Examiners report

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

Syllabus sections

Topic 4 - Statistical applications » 4.4
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