### 2.9 Use statistical methods to make an inference

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 Achievement Objective 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. A glossary of statistical terms may be useful for learners.

Note, Level 7 concepts:

- 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.
- Making a call at level 5-7

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