Achievement objective S8-2
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
- Make inferences from surveys and experiments:
- A. determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem
- B. using methods such as resampling or randomisation to assess the strength of evidence.
Indicators
Note: there are significant changes here in approach and content.
The approach to teaching confidence intervals may be entirely based on a
simulation using technology, as will be the methods for
resampling.
See
Census at School for further information and resources.
A. Determining estimates and confidence intervals for means, proportions, and differences, recognising the relevance of the central limit theorem.
- Within the context of an
investigation and
statistical plots of observed data:
- determines and interprets confidence intervals in a range of situations and draws relevant conclusions with justification.
B. Using methods such as resampling or randomisation to assess the strength of evidence:
- Within the context of an
investigation and
statistical plots of observed data:
- estimates a parameter in a sampling situation using bootstrapping (a re-sampling method)
- determines and interprets the
strength of evidence for a claim in an experimental situation using a randomisation test
- draws a conclusion with justification.
Progression
S8-2 links from S7-2.
What is new/changed?
- Difference of medians.
- Resampling and randomisation methods will be used to generate confidence intervals and to assess the strength of evidence; this means that the central limit theorem is de-emphasised as a basis for confidence intervals. Rather the focus is on the logic behind inference. Computer use for these methods is essential.
Possible context elaborations
- In an
experiment, students are
randomly assigned to sit or stand
treatments. Does the pulse rate of the students who are standing tend to be higher than that of those who are sitting?
- In a well-designed sample survey, a random sample of year 13 students in New Zealand was asked many questions about their lifestyle. Investigate: What proportion of year 13 students eats breakfast at least five times a week back in the population? Is there an association between year 13 students eating breakfast at least five times a week and their perception of whether they have a healthy lifestyle?
Assessment for qualifications
NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
NZQA website.
The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.
Learn more:
Note: Aligned and registered level 3 achievement standards will not be on the NZQA website until December 2012.
- School planning draft level 3 achievement standards are on
NCEA on TKI.
- Final draft level 3 achievement standards will be on
NCEA on TKI from end of September.
- Aligned level 3 achievement standards will be registered and published by NZQA for use in 2013 in December.
Full information on the level 3 draft standards and the alignment process can be found on
NCEA on TKI.
The following achievement standard(s) could assess learning outcomes from this AO:
- AS91582 Mathematics and statistics 3.10 Use statistical methods to make a formal inference; Internal, 4 credits.
- AS91583 Mathematics and statistics 3.11 Conduct an experiment to investigate a situation using experimental design principles; Internal, 4 credits.
Refer to the draft standards matrix.
Last updated March 5, 2013
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