# Mathematics and Statistics - annotated exemplars level 2 AS91264

## Use statistical methods to make an inference (2.9)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 796KB)

This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

Last updated July 2019.

There is new student evidence and annotations for all grade boundaries.

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 147KB)

For Excellence, the student needs to use statistical methods to make an inference, with statistical insight.

This involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle which may involve reflecting on the process, or considering other explanations.

The student has integrated statistical and contextual knowledge throughout the statistical enquiry cycle (1), provided some evidence of considering other explanations (2) and reflected on the process (3).

For a more secure Excellence, the student could provide further reflection on the process by developing the discussion on taking another sample and making the same claim. For example, the student could explain why the same claim would be expected from different samples.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 122KB)

For Merit, the student needs to use statistical methods to make an inference, with justification.

This involves linking components of the statistical enquiry cycle to the context, and/or to the populations, and referring to evidence such as sample statistics, data values, trends, or features of visual displays in support of statements made.

This student’s evidence comes from the TKI assessment resource ‘The Great Debate’.

The student has linked the components of the statistical enquiry cycle to the context and population (1), and provided supporting evidence for the statements made (2).

To reach Excellence, the student could demonstrate a clearer understanding about sampling variability, and include some reflection on the process. Additional integration of statistical and contextual knowledge would also be expected, for example linking the conclusion back to the introduction.

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 109KB)

For Merit, the student needs to use statistical methods to make an inference, with justification.

This involves linking components of the statistical enquiry cycle to the context, and/or to the populations, and referring to evidence such as sample statistics, data values, trends, or features of visual displays in support of statements made.

This student’s evidence comes from the TKI assessment resource ‘The Great Debate’.

The student has provided supporting evidence for statements made (1), and provided some evidence of linking the components of the statistical enquiry cycle to the context and to the population.

For a more secure Merit, the student could provide stronger evidence of linking the components of the statistical enquiry cycle to the context, and to the population. For example, the discussion of the sampling distributions could be linked more clearly to the context by ensuring that the comments refer to reaction times.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 207KB)

For Achieved, the student needs to use statistical methods to make an inference.

This involves showing evidence of using each component of the statistical enquiry cycle to make an inference.

This student’s evidence comes from the TKI assessment resource ‘The Great Debate’.

The student has posed an appropriate investigative comparison question (1), selected random samples (2), selected and used appropriate displays and measures (3), discussed sample distributions (4), discussed sampling variability, including the variability of estimates (5), made an inference (6), and communicated findings in a conclusion (7).

To reach Merit, the student could justify the call with specific evidence from the displays, and include the actual population with the interval estimates for the population medians.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 200KB)

For Achieved, the student needs to use statistical methods to make an inference.

This involves showing evidence of using each component of the statistical enquiry cycle to make an inference.

This student’s evidence comes from the TKI assessment resource ‘The Great Debate’.

The student has posed an appropriate investigative comparison question (1), selected random samples (2), selected and used appropriate displays and measures (3), discussed sample distributions (4), discussed sampling variability, including the variability of estimates (5), made an inference by giving an interval estimate for the median time standing on the left leg (6), and communicated findings in a conclusion (7).

For a more secure Achieved, the student could use the informal confidence intervals to make a comparative statement about the median times for the two population groups standing on the left leg.

The student could also provide stronger evidence of discussing the sample distributions in context by referring to the times standing on the left leg, and include the variable with both interval estimates.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 294KB)

For Achieved, the student needs to use statistical methods to make an inference.

This involves showing evidence of using each component of the statistical enquiry cycle to make an inference.

This student’s evidence comes from the TKI assessment resource ‘SURFing’.

The student has posed an investigative comparison question (1), selected random samples (2), selected and used appropriate displays and measures (3), discussed sample distributions (4), discussed sampling variability, including the variability of estimates (5), and communicated findings in a conclusion (6).

To reach Achieved, the student would need to make an inference by answering the investigative question about the median weekly incomes in the population. An understanding of the comments about weekly incomes applied to 2001 should also be evident.