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Exam-Style Question on Significance

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Question id: 18. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

The older students from Glee High School are required to follow a two year IB Mathematics course. Data were gathered from a sample of 242 students regarding their choice of course. The following data were recorded.


A \(\chi ^2\) test was carried out at the 5% significance level to analyse the relationship between gender and choice of mathematics course.

(a) Write down the null hypothesis, Ho, for this test.

(b) Find the expected value of female students on the Studies course.

(c) Write down the number of degrees of freedom.

(d) Use your graphic display calculator to determine the \(\chi ^2\)calc value.

(e) Determine whether Ho should be accepted. Justify your answer.

One student is chosen at random from the 242 students.

(f) Find the probability that this student is male.

(g) Find the probability that the student chosen at random is on the Standard course.

Two students are chosen at random from the 242 students.

(h) Find the probability that both are on the Studies course.

(i) Find the probability that neither are on the Higher course.

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If you are using a TI-nSpire CX calculator and you would like to see an example of the process used in this question see GDC Essentials.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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