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Achievement Standard 
Achievement Standard 2.9 #91264 (link to NZQA) 
NZ Curriculum Achievement Objectives 
• carry out investigations of phenomena, using the statistical enquiry cycle: using existing data sets evaluating the choice of sampling and data collection methods used using relevant contextual knowledge, exploratory data analysis, and statistical inference • make inferences from surveys: 
Explanation 
Use statistical methods to make an inference involves showing evidence of using each component of the statistical enquiry cycle to make an inference. Use statistical methods to make an inference, with justification 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. Use statistical methods to make an inference, with statistical insight involves integrating statistical and contextual knowledge throughout the statistical enquiry cycle which may involve reflecting on the process, or considering other explanations. 
Content 
The process of investigating a situation by experiment involves:

ClarificationsAn important understanding is that the random samples are being used to talk about the population groups. There needs to be clear links between the investigative question, the analysis and the conclusion. ProblemThe purpose of the investigation needs to be clear. Students must demonstrate an understanding of the population from which the sample will be taken. The investigative question that is posed must involve a comparison. The investigative question needs to:
A suitable question would be Is the median height of NZ year 12 boys greater than the median height of NZ year 12 girls? Plan and DataThe investigation involves selecting random samples from the population groups and using information from the samples to make an inference about the population groups. AnalysisThe informal confidence intervals for the population medians are required and need to be used to answer the comparison investigative question. At Achieved level it is sufficient to show the informal confidence intervals on the graph. At Merit level and above the informal confidence intervals must be given in context. For example, ‘I am pretty sure that the median height for NZ year 12 boys is somewhere between xxx and yyy'. In discussing the sample distributions, the discussion must be about the distributions of the variables, for example the heights of NZ year 12 boys and NZ year girls. The discussion needs be in context at all levels. The context includes the variable, for example height, numerical values and associated units and the population groups. ConclusionStudents must make an inference, which will be a conclusion about the population medians based on their samples taken from the population. The conclusion must be consistent with the analysis. It will answer the posed investigative question and will involve making a call about the population medians. The informal confidence intervals will be used to make an inference about the population medians. If there is no overlap in the informal confidence intervals an appropriate inference is that the population median for ‘A’ is greater than the population median for ‘B’. If there is an overlap in the informal confidence intervals there is not enough evidence to make a call that the population median for ‘A’ is greater than the population median for ‘B’. At Merit and above, an interpretation of the informal confidence intervals are required. An understanding relating to sampling variability and variability of estimates must be evident. Another sample will give different medians and informal confidence intervals 
The key idea of statistical literacy at level 7 is being a critical consumer of data at a societal level. At level seven students are working with a variety of statistically based reports. The types of reports have become more specialised in terms of the statistics and/or probability presented in them. Things like risk, relative risk, sampling and nonsampling errors need to be present in these reports. Students should be using the level 7 critical questions as they evaluate these reports. Students should be linking the ideas for statistical literacy with what they have done in statistical investigations and probability at level 7. Polls and surveys are considered at this level leading to experiments and observational studies in level eight. This key idea develops from the key idea of statistical literacy at level 6 where students can interpret media type data reports. 