Apps. and Interpretation for IBDP Maths Ebook 1 | Page 346

Your Practice Set – Applications and Interpretation for IBDP Mathematics
97
Paper 1 – Tests for Independence
Example
Mateo is a Science teacher who wishes to investigate the relationship between the Physics
grades and Chemistry grades of all 160 Science students in the school.
The following table shows the distribution of the grades (A, B and C) for the students:
Physics
Chemistry
A B C
A 13 22 10
B 25 30 11
C 27 12 10
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 �
2
calc
The critical value is given by 9.488.
, the test statistic.
[2]
[1]
[2]
(d)
State the conclusion of the test with a reason.
[2]
Solution
(a) (i) H
0
: The grade in Physics and the grade in
Chemistry are independent. A1 N1
(ii) H
1
: The grade in Physics and the grade in
Chemistry are not independent. A1 N1
(b) 4 A1 N1
[2]
[1]
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