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

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.

Gender | Studies | Standard | Higher | Total |

Male | 35 | 15 | 21 | 71 |

Female | 60 | 30 | 81 | 171 |

Total | 95 | 45 | 102 | 242 |

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, H_{o}, 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 H_{o} 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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