## Exam-Style Question on Significance## A mathematics exam-style question with a worked solution that can be revealed gradually |

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, H_{o}, 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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