# Level 3

## 91582: Use statistical methods to make a formal inference

Updated April 2020. The sections ‘Posing an appropriate comparison investigative question using a given multivariate data set’ and ‘Making an appropriate formal statistical inference’ have been updated. The section ‘Communicating findings in a conclusion’ has been added.

Students need to provide evidence of each component of the statistical enquiry cycle detailed in Explanatory Note 3 of the standard.

### Posing an appropriate comparison investigative question using a given multivariate data set

Sufficient time needs to be allocated for students to research the context and acquire appropriate and relevant contextual knowledge. For all grades, students need to identify a purpose and pose an investigative question which is informed by this contextual knowledge. The question needs to ask what the difference is between the population parameters. It needs to include the population under investigation.

An appropriate question could be: 'For New Zealand Telco users 18 years and over in 2017, what is the difference between the median number of text messages sent per day by adults and the median number of text messages sent per day by teenagers?'

### Discussing sample distributions

Students need to discuss, in context, what they see in the displays of the sample distributions. This could include central tendency, spread, shift and unusual values.

Discussing sampling variability including the variability of estimates

Students need to show an understanding that if they were to take another sample from the population this is likely to result in different displays and summary statistics.

### Making an appropriate formal statistical inference

Students need to use the bootstrap confidence interval for the difference in the medians/means to answer their investigative question. The formal statistical inference will be an interval estimate for the difference in the means or medians of the population groups. Students also need to show an understanding about the nature of the confidence interval.

An appropriate formal statistical inference could be: ‘I am fairly sure that, for New Zealand Telco users 18 years and over in 2017,  the median number of text messages per day sent by adults is somewhere between 12 and 17 greater than the median number of text messages per day sent by teenagers.’

### Communicating findings in a conclusion

The findings in the conclusion would then include this call from the formal statistical inference:

‘I am fairly sure that, for New Zealand Telco users 18 years and over in 2017, the median number of text messages per day sent by adults was greater than the median number of text messages per day sent by teenagers.’

### Required quality of student response

For Merit, students need to justify all findings with reference to evidence from the displays and statistics and link the purpose and findings to their research.

For Excellence, students need to integrate the statistical and contextual knowledge, gained from their research, throughout the response. This may include reflecting on the process or considering other relevant explanations.