# Mathematics and Statistics - annotated exemplar Level 3 AS91582 (B)

## Use statistical methods to make a formal inference (3.10B)

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 See EXEMPLAR A for this standard TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 552KB)

### Low Excellence

Commentary
Student response

Student 1 (PDF, 252KB)

For Excellence the student is required to use statistical methods to make a formal inference, with statistical insight. This involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle and reflecting on the process.

There is evidence that statistical and contextual knowledge have been integrated.

The student has used their research to develop a purpose and to pose an appropriate question (1). The Los Angeles research that is referenced is not directly related to drivers.

Analysis comments are clearly linked to the context (highlighted) and there is some consideration of other explanations.

For a more secure Excellence the student would need to investigate the data more fully. For example, a consideration of other variables and research findings needs to be more directly related to the question.

### High Merit

Commentary
Student response

Student 2 (PDF, 122KB)

For Merit the student is required to use statistical methods to make a formal inference, with justification. This involves linking components of the statistical enquiry cycle to the context and making supporting statements which refer to evidence.

There is evidence of some research related to the purpose and a comparison question has been posed (1).

While the population is not clear in the question, it is clear in the conclusion.

The discussion has been linked to the context throughout (highlighted) and the conclusion has been clearly justified (2).

There is some evidence of insight in the comment "Something I found unusual...", but in order to reach Excellence there needs to be more evidence of statistical insight.

### Low Merit

Commentary
Student response

Student 3 (PDF, 114KB)

For Merit the student is required to use statistical methods to make a formal inference, with justification. This involves linking components of the statistical enquiry cycle to the context and making supporting statements which refer to evidence.

An explanation for the choice of variables has been given, and an appropriate question that identifies the population and the difference between the medians of the two groups has been posed (1).

Some of the discussion on the distributions has been linked to the context or investigative question (highlighted). The comment on unusual features is unclear and the reference to the range is incorrect.

The student has made a correct call ("Based on my samples…") that has been justified.

For a more secure Merit the linking of the analysis discussion to the population needs to be developed, and more than a minimal statement on representativeness and sampling variability would be expected.

### High Achieved

Commentary
Student response

Student 4 (PDF, 86KB)

For Achieved the student is required to use statistical methods to make a formal inference, showing evidence of using each component of the statistical enquiry cycle.

The student has provided evidence for each component of the statistical enquiry cycle to make a formal inference.

While there is some linking of the analysis comments back to the context (highlighted), the evidence for this aspect of the cycle needs to be clearer in order to reach Merit.

### Low Achieved

Commentary
Student response

Student 5 (PDF, 161KB)

For Achieved the student is required to use statistical methods to make a formal inference, showing evidence of using each component of the statistical enquiry cycle.

A comparison question ("Do high risk…") has been posed, but it does not include looking at the difference in the medians between the two population groups. The population in the question is unclear, but it is given in the background information and there is a reference to the difference in the medians in the conclusion (1).

Summary statistics have not been given.

In the analysis comments there is an attempt to link back to the context (highlighted).

The confidence interval has been correctly interpreted and used to make a correct call (1).

For a more secure Achieved the question needs to identify the population and make reference to the difference in the medians.

### High Not Achieved

Commentary
Student response

Student 6 (PDF, 53KB)

For Achieved the student is required to use statistical methods to make a formal inference, showing evidence of using each component of the statistical enquiry cycle.

The comparison question does not identify looking at the difference in the population medians and the population is not completely clear (1).

While there are descriptive comments about the sample distributions, the units ("milligrams") are incorrect, and there is no attempt to discuss what the observations mean.

The interpretation of the confidence interval ("After 1000 bootstrapping…") in the first paragraph of the analysis is incorrect.

The student has made an appropriate formal statistical inference and used the inference to make a correct call (2).

To reach Achieved the analysis discussion would need to be more clearly linked back to the context and the question would be improved.