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# P

##### Problem, Pose a Question

The purpose of the investigation needs to be clear.
It must show an understanding of the population from which the sample will be taken.
The investigative question that is posed must involve a comparison.

- Identify the variables, for example gender and height,
- Identify the population groups, for example NZ year 12 girls and NZ year 12 boys.
- Identify the population parameter.
- Include a statement about a population parameter which will give an indication of what you think the result will be, for example NZ year 12 boys are taller than NZ year 12 girls. (the direction of the comparison)

Research the context of the situation.
Make a prediction and justify your prediction
'There is a belief that...'
'I want to test the claim that...'

'I wonder if the median (variable) from (group A, population A) tends to be larger than the median from (group B, population B)'

'Is the median height of NZ year 12 boys greater than the median height of NZ year 12 girls?'

# P

##### Plan

Define your chosen variables and explain why you have selected them and the background context.

# D

##### Display

Using the sample data display a dot plot and box and whisker plot and discuss features of the sample distribution and the sample statistics

# A

##### Analysis

Use iNZight software to make a bootstrap confidence interval for the difference between population medians and make a comparison between the groups being investigated (statistical inference)

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.

Discussion of the difference in the medians with contextual links back to the population and an indication of uncertainty
'I can be reasonably sure that...'

Be sure to be clear when you are discussing the sample and when you are discussing the population estimate.

# C

##### Conclusion

Make a conclusion communicating your findings (answering your statistical comparison question, with mathematical justification.

You must make an inference, which will be a conclusion about the population medians based on their samples taken from the population.

Your conclusion 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.

Discuss sampling variability, including the variability of the population estimates.
An understanding relating to sampling variability and variability of estimates must be evident. Another sample will give different medians and informal confidence intervals.

###### Link to census at school PPDAC page

Exploring Data Web site