Achievement objective S72
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. making informal predictions, interpolations, and extrapolations
 B. using sample statistics to make point estimates of population parameters
 C. recognising the effect of sample size on the variability of an estimate.
Indicators
Note: this content is new to the statistics curriculum.
See
CensusAtSchool under informal inference for further information and resources. At level 7, B, and C (below) are critical for students to advance to level 8.
A. Making informal predictions, interpolations, and extrapolations:
 Within the context of an
investigation and
statistical plots of observed data:
 Uses a scatterplot from a sample to make sensible predictions within the given data by plotting the trend informally by eye and showing likely variation band for a particular value of x, the explanatory variable.
 Informally extrapolates where appropriate and predicts the trend outside the given data values on a scatterplot and justifies using contextual understanding.
B. Using sample statistics to make point estimates of population parameters.
 Understands that the sample statistics can be used as point estimates of the population parameters, for example, sample medians and IQRs can be used as point estimates for population medians and IQRs, or sample proportions for population proportions when using categorical data.
C. Recognising the effect of sample size on the variability of an estimate:
 Within the context of an
investigation and
statistical plots of observed data:
 Finds informal confidence intervals for population medians.
 Plots sample data showing informal confidence intervals (median ± 1.5 IQR / √n) on boxplots.
 Uses an informal confidence interval to make an
inference about the population median from sample data plot.
 Makes a claim about whether one group has larger values than another group using informal confidence intervals for the population medians.
 Explains the connections among sample, population,
sampling variability,
sample size effect, informal confidence interval, and degree of confidence.
Progression
S72 links from S61 and to S71, S73, S82.
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What is new/changed?
 Statistical inference.
 Informal confidence intervals for population medians.
 The effect of sample size on the variability of an estimate.
 Using relevant contextual knowledge (given).
Possible context elaborations

CensusAtSchool is a valuable website for classroom activities and information for teachers on all things statistics.
 Do year 12 students carry heavier bags than year 9 students? If Jane took a random sample of size 30 and Emma took a random sample of size 100, explain in words and pictures how their confidence intervals would differ and why.
 Reaction time vs age for students aged 8 to 18. Is it reasonable to assume that reaction time will continue to decrease at a steady rate after 18? What do we expect reaction time for very young children or very old people to be? If we want to predict the reaction time of a tenyearold, what does the data suggest is a sensible prediction band?
 Kiwi Kapers (see context elaborations for
S71)
Assessment for qualifications
NCEA achievement standards at level 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 following achievement standard(s) could assess learning outcomes from this AO:
 AS91264 Mathematics and statistics 2.9 Use statistical methods to make an inference
 AS91265 Mathematics and statistics 2.10 Conduct an experiment to investigate a situation using statistical methods
Refer to the
mathematics and statistics matrix.
Last updated September 26, 2013
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