Table 6 shows achievements of students who pass Mathematics and Science subjects in a primary school examination. There is a claim that students who perform well in Mathematics subject will also have good grade in Science subject. At α = 0.05, show that if there is any relationship between students’ achievement in Mathematics and Science subjects.

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Table 6 shows achievements of students who pass Mathematics and Science subjects in a primary
school examination. There is a claim that students who perform well in Mathematics subject will
also have good grade in Science subject. At α = 0.05, show that if there is any relationship
between students’ achievement in Mathematics and Science subjects.
Table 6

(i) State the null and alternative hypotheses.
(ii) Calculate test statistic by clearly showing each step in the calculation.
(iii) Is there any evidence on the relationship between achievements of Mathematics and
Science subjects?

  Achievement (%) Achievement(%) Achievment(%) Achievment(%)
Subjects/Grade A B C D
Mathematics 14.7 18.3 18.4 27.0
Science 6.8 32.0 36.2 19.4
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