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Date May Example question Marks available 3 Reference code EXM.1.SL.TZ0.10
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Explain Question number 10 Adapted from N/A

Question

Give your answers to four significant figures.

A die is thrown 120 times with the following results.

Showing all steps clearly, test whether the die is fair

(i)   at the 5% level of significance;

(ii)  at the 1% level of significance.

[7]
a.

Explain what is meant by “level of significance” in part (a).

[3]
b.

Markscheme

The data can be described by the following table

       (A1)

H0: the die is fair H1: the die is not fair}      (C1)

χ2calc=(2027)220+(1220)220+(1620)220+(2520)220+(2620)220+(1420)220

=11.3       (A1)

 

(i)  χ20.95;5=11.07       (A1)

     Hence, since 11.3 > 11.07 at the 5% level we must accept H1.       (R1)

 

(ii) χ20.99;5=15.086       (A1)

     Hence, since 11.3 < 15.086, at the 1% level, there is not enough evidence to conclude that the die is not fair (and hence we accept H0).       (R1)

 

[7 marks]

a.

Let α denote the significance level. If χ2calc is greater than χ2α,n1 then it means that the probability of obtaining the results obtained is less than α if H0 is correct.        (R3)

Note: Award (R3) for any correct explanation. Use discretion to award (R2) or (R1).

[3 marks]

b.

Examiners report

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

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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