Exam-Style Question on Significance

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 89. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

A group of students were asked how they get to school each day. The results are shown in the following table

 Walk Bicycle Car Bus Total Male 22 36 35 56 149 Female 32 46 45 50 173 Total 54 82 80 106 322

A $$\chi^2$$ test was preformed to see if there was a connection between gender and the method of travelling to school.

(a) Write down what the null hypothesis, Ho, might have been for this test.

(b) Find the expected frequency for the females who cycle to school.

(c) Find the $$\chi^2$$ statistic.

(d) State whether or not the null hypothesis is accepted at a 5% significance level. Give a reason for your answer.

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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.

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