Apps. and Interpretation for IBDP Maths Ebook 1 | Seite 347

(c)
� � 8.968013758
(A1) for correct value
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� � 8.97
A1 N2
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(d) The null hypothesis is not rejected. A1
2
As � � 9.488 . A1 N2
calc
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Exercise 97
1. A Mathematics teacher carried out an investigation of the results of the annual
Mathematics examination. The examination paper consists of three sections: Algebra,
Geometry and Statistics. A student can get a pass in a section if at least half of the
answers are correct in that section.
The following table shows the number of students who passes or fails in each section:
Results
Sections
Algebra Geometry Statistics
Pass 12 5 18
Fail 8 15 2
A
2
� test for independence is conducted at a 5% significance level.
(a) (i) Write down the null hypothesis of the test.
(ii) Write down the alternative hypothesis of the test.
(b) Write down the degree of freedom of the test.
(c) Find the value of �
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The critical value is given by 5.991.
, the test statistic.
[2]
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(d)
State the conclusion of the test with a reason.
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