## Exam Style Question## Worked solutions to typical exam type questions that you can reveal gradually |

Question id: 16. This question is similar to one that appeared in an IB Studies paper in 2010. The use of a calculator is allowed.

One hundred and sixty students are asked how many portions of fruit or vegetables on average they have per day. The data collected is organized in the following table.

2 or fewer | 3 or 4 | More than 4 | Total | |

Male | 25 | 35 | 25 | 85 |

Female | 22 | 30 | 23 | 75 |

Total | 47 | 65 | 48 | 160 |

A \(\chi ^2\) test is carried out at the 5% level of significance.

(a) Write down the null hypothesis, H_{o}, for this test.

(b) Write down the number of degrees of freedom for this test.

(c) Find the \(\chi ^2_{calc}\) value for this data.

(d) Find the expected number of females that have more than 4 portions per day (correct to the nearest integer).

(e) Decide whether H_{o} must be accepted.

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