This internal Achievement Standard is derived from Achievement Objective S7.1, Carry out investigations using the statistical enquiry cycle.

In particular, using existing data sets,

- evaluating the choice of sampling and data collection methods used
- using relevant contextual knowledge, exploratory data analysis, and statistical inference,

and S7.2, Make inferences from surveys,

- using sample statistics to make point estimates of population parameters
- recognising the effect of sample size on the variability of an estimate.

Using an existing data set of population data, students will pose an investigative comparison question, select random samples, use appropriate displays and measures, discuss sampling distributions and variability including the variability of estimates. They will use sample statistics to make point estimates of population parameters and make an inference. Attention should be paid to the shape of sampling distributions and whether or not samples overlap. It is important throughout the statistical enquiry cycle to consider the context of the data.

Note,

- statistical inference – the process of drawing conclusions about population parameters based on a sample taken from the population.
- sampling error – the error caused because data are collected from part of population (even if a sample is unbiased), rather than the whole population.

## Achievement standard and Guides

- Achievement Standard (AS91264) 2015
- NZQA Exemplars, assessments and reports
- Clarification of the Standard (AS91264)
- Conditions of assessment
- Moderator’s newsletter comments regarding posing comparative questions July 2012
- Senior Secondary Guide AO S7-1
- Senior Secondary Guide AO S7-2
- Sample to population inference progressions
- Guidelines for “How to make the call”
- Key Ideas in Statistical Literacy
- Glossary of Statistics terms

## FAQ

**Kiwi Kapers, I wonder what is the median weight of kiwis? How should I encourage my students to write conclusions when making an inference?****Can you please clarify the definition of a sampling error as students often get confused between sampling error and non-sampling error?****How do I correctly pose a comparison investigative question for Kiwi Kapers 3 and state my conclusions when making an inference about the population?****Why have there been so many changes to the Statistics Curriculum, especially with regards to the Central Limit Theorem and Confidence Intervals?****What is the name of the error bounds for the sample median?****What possible relevance can statements about the sample be in helping us draw a conclusion about the population?****Can we make the assumption that C@S data is a population?**

## Resources for teaching and learning

### Key Resources

**Sample to population inference - The Path to 3.10****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Inference Pain Points - Robyn Headifen****FAQs for Inferential thinking****Animations of sampling variation****Visualising sampling variation at Level 7****Guidelines for "How to make the call"**

### Teacher Preparation

**Teaching research for NCEA L2 and L3 Statistics****Strategies, tools and prompts to support statistical report writing****Fitting data collection into your Stats lessons****Sample to population inference - The Path to 3.10****Confidence Intervals developing big ideas - Dr Dalrymple's Blog****Inference Pain Points - Robyn Headifen****FAQs for Inferential thinking****Animations of sampling variation****Caught in the path of the data deluge****Statistics Education 21st Century NZ****Building inferential reasoning in statistics Part 1****A teachers's guide to informal comparative reasoning****Laying the foundations for inference****Teaching activities for Achievement Standard 2.9****Statistical Concepts Unpacked****Difficulties in learning about sampling variability, and teacher approaches to overcome these****Visualising sampling variation at Level 7****Issues in Level 2 NCEA: Use statistical methods to make an inference AS 91264****Guidelines for "How to make the call"****Statistical thinking in empirical theory****Training teachers in statistical thinking****Telling Data Stories: Essential Dialogues for Comparative Reasoning****Developing Statistical Literacy**

### Classroom Activities

**Enriching sampling decisions in NCEA Level 2****Making sense of the meaningful data all around us!****Sampling variation just keeps turning up everywhere!****Analysing Student Attendance Data****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Teaching activities for Achievement Standard 2.9****Visualising sampling variation at Level 7****iNZight instructions 3 (Bear hugs 3)****Finding Informal Confidence Intervals****Informal statistical inference revisited****Property sales in North Shore city****Engaging with shape****Data card sampling from a population Yr 9-12****Inference writing frame****Kiwi Kapers 1****To tag or not to tag?**

### Datasets

**SURF data sets****CensusAtSchool 2009 data subset (15,000 rows)****CensusAtSchool 2007 data subset (15,000 rows)****NZ Incomes 2003 SURF**