# Chi-squared Faker

### Why do this problem?

This problem gives students an insight into the fact that data can be manipulated to give conflicting results and a glimpse of the more difficult issues surrounding the study of statistics. It contains a good mathematical problem solving element and draws students into the workings of the Chi-squared test, resulting in a greater understanding of the mechanics of the test.

### Possible approach

Key to this task is the realisation that the Chi-squared test requires grouping of data classes when individual classes contain few elements and, in this case, that there are a variety of equally sensible ways of grouping the data. Students might realise this individually or this might emerge through classroom discussion.

### Key questions

• Can you think of a convincing explanation for the expected distribution of weights?
• What choices are there to be made in a Chi-squared calculation?
• How would you group classes to most increase the Chi-squared statistic?

### Possible extension

If students have access to a spreadsheet, they might try to invent their own set of data which exhibits this type of behaviour.

### Possible support

Rather than try to work out which would be the best grouping before performing a calculation, suggest that different students cluster the data categories individually and then perform the standard Chi-squared test. The students could then compare results and hopefully then realise that the grouping can significantly affect the character of the result.