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Date November 2018 Marks available 1 Reference code 18N.1.SL.TZ0.T_4
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term State Question number T_4 Adapted from N/A

Question

Abhinav carries out a χ2 test at the 1 % significance level to determine whether a person’s gender impacts their chosen professional field: engineering, medicine or law.

He surveyed 220 people and the results are shown in the table.

State the null hypothesis, H0, for this test.

[1]
a.

Calculate the expected number of male engineers.

[2]
b.

Find the p-value for this test.

[2]
c.

Abhinav rejects H0.

State a reason why Abhinav is incorrect in doing so.

[1]
d.

Markscheme

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

gender and chosen profession are independent       (A1) (C1)

Note: Accept there is no association between chosen profession and gender. Accept “not dependent”. Do not accept “not related” or “not correlated” or “not influenced”, or “does not impact”.

 

[1 mark]

a.

110 220 × 90 220 × 220     ( 110 × 90 220 )        (M1)

Note: Award (M1) for correct substitution into expectation formula.

= 45       (A1) (C2)

 

[2 marks]

b.

0.0193 (0.0192644…)      (A2) (C2)

 

[2 marks]

c.

0.0193 > 0.01  (1%)       (A1)(ft)

OR

the p-value is greater than the significance level  (1%)         (A1)(ft) (C1)

 

Note: A numerical value in (c) must be seen to award the (A1)(ft). Follow through from part (c), only if it is > 0.01.

Accept a correct answer from comparing both the numerical value of the Χ2 statistic and the numerical value of the critical value: 7.89898… < 9.21.

 

[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 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
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Topic 4—Statistics and probability

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