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Date May 2019 Marks available 2 Reference code 19M.2.SL.TZ1.T_3
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Calculate Question number T_3 Adapted from N/A

Question

A survey was conducted on a group of people. The first question asked how many pets they each own. The results are summarized in the following table.

The second question asked each member of the group to state their age and preferred pet. The data obtained is organized in the following table.

A χ 2 test is carried out at the 10 % significance level.

Write down the total number of people, from this group, who are pet owners.

[1]
a.

Write down the modal number of pets.

[1]
b.

For these data, write down the median number of pets.

[1]
c.i.

For these data, write down the lower quartile.

[1]
c.ii.

For these data, write down the upper quartile.

[1]
c.iii.

Write down the ratio of teenagers to non-teenagers in its simplest form.

[1]
d.

State the null hypothesis.

[1]
e.i.

State the alternative hypothesis.

[1]
e.ii.

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

[1]
f.

Calculate the expected number of teenagers that prefer cats.

[2]
g.

Use your graphic display calculator to find the p -value for this test.

[2]
h.

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

[2]
i.

Markscheme

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

140       (A1)

[1 mark]

a.

1       (A1)

[1 mark]

b.

2       (A1)

[1 mark]

c.i.

1       (A1)

[1 mark]

c.ii.

3       (A1)

[1 mark]

c.iii.

17:15  OR   17 15       (A1)

Note: Award (A0) for 85:75 or 1.13:1.

[1 mark]

d.

preferred pet is independent of “whether or not the respondent was a teenager" or "age category”     (A1)

Note: Accept there is no association between pet and age. Do not accept “not related” or “not correlated” or “influenced”.

[1 mark]

e.i.

preferred pet is not independent of age    (A1)(ft)

Note: Follow through from part (e)(i) i.e. award (A1)(ft) if their alternative hypothesis is the negation of their null hypothesis. Accept “associated” or “dependent”.

[1 mark]

e.ii.

3    (A1)

[1 mark]

f.

85 × 55 160   OR   85 160 × 55 160 × 160      (M1)

29.2 (29.2187…)      (A1)(G2)

[2 marks]

g.

0.208 (0.208093…)      (G2)

[2 marks]

h.

0.208 > 0.1      (R1)

accept null hypothesis  OR  fail to reject null hypothesis      (A1)(ft)

Note: Award (R1) for a correct comparison of their p -value to the significance level, award (A1)(ft) for the correct result from that comparison. Accept “ p -value > 0.1” as part of the comparison but only if their p -value is explicitly seen in part (h). Follow through from their answer to part (h). Do not award (R0)(A1).

[2 marks]

i.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
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Topic 4—Statistics and probability

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