# 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: 16. This question is similar to one that appeared on 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, Ho, 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 Ho must be accepted.

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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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