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# 2.9 Achievement Objectives AS 91264

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

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:

• posing an investigative question about a given experimental situation

• planning the experiment by

• determining appropriate variables and measures

• determining data collection and recording methods

• conducting the experiment and collecting data

• selecting appropriate displays and measures

• discussing displays and measures

• communicating findings in a conclusion.

### Clarifications

An 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.

### Problem

The 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:

• identify the variables, for example gender and height
• identify the population groups, for example NZ year 12 girls and NZ year 12 boys
• include a statement about a population parameter which will give an indication of what the student thinks the result will be, for example NZ year 12 boys are taller than NZ year 12 girls
• identify the population parameter.

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 Data

The investigation involves selecting random samples from the population groups and using information from the samples to make an inference about the population groups.

### Analysis

The 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.

### Conclusion

Students 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