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# Activity: Legal driving age

## Purpose

Students will investigate possible explanations for reasons behind an opinion that the legal driving age should be raised to at least 18 years.

## Achievement objectives

• S8-1: Carry out investigations of phenomena, using the statistical inquiry cycle:
• A. conducting surveys
• C. using informed contextual knowledge, exploratory data analysis, and statistical inference
• D. communicating findings and evaluating all stages of the cycle.
• S8-2: 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.
• S8-3: Evaluate a wide range of statistically based reports, including surveys and polls, experiments, and observational studies:
• A. critiquing causal-relationship claims.

## Indicators

Uses the statistical enquiry cycle.

• Conducts surveys to find solutions to problems:
• Poses investigative questions to explore using the statistical inquiry cycle.
• Collects own survey data using a questionnaire.
• Uses an appropriate sampling method.
• Uses exploratory data analysis to unlock the stories in the data:
• Uses appropriate statistical graphs and tables to explore the data and communicates relevant detail and overall distributions.
• Explores other variables or groupings to look for patterns and relationships.
• Uses appropriate measures to communicate features of the data.
• Uses informed contextual knowledge to support explanations and to communicate findings.
• Makes statistical inferences.
• Communicates findings:
• Support (or otherwise) for original hypothesis or conjecture.
• Appropriate graphs that relate to findings discussed in conclusion.
• Quantifies summary statistics to support (or otherwise) the conjecture.
• Population to which the findings can be generalised.
• Constraints of the experiment or survey within which the findings are valid.
• Alternative explanations.
• Evaluates all stages of the cycle:
• Specifies, justifies, and relates improvements (contextual or statistical) to the problem.

The approach to teaching confidence intervals may be entirely based on a simulation using technology, as will be the methods for resampling.

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:
• determines and interprets the strength of evidence for a claim using a method for resampling in a range of situations and draws a conclusion with justification about whether observations are real or due to chance variation alone.

## Specific learning outcomes

Students will be able to:

• use all stages of the PPDAQ cycle to carry out a statistical investigation.

## Diagnostic snapshot(s)

Students read the article from The New Zealand Herald suggesting that 80% of New Zealanders support a legal driving age of 18 years or higher. In small groups, students discuss the claims made.

• Do they think the support for increasing the legal driving age is truly 80%?
• How might they investigate whether the claim is likely to be true?

## Planned learning experiences

Students read an article from the NZ Herald ( Driving age of 18 makes perfect sense) suggesting that 80% of New Zealanders support a legal driving age of 18 years or higher. In small groups, students discuss the claims made and find that there is merely anecdotal evidence for these reasons.

Students discuss in groups other reasons that might underpin these opinions and how they could find out what the reasons might be. For example:

• Parents could be worried about their children who are learning to drive. This might result in a different proportion of parents and non-parents in their views.
• People might be worried about their own safety with younger drivers on the road. This might result in a similar proportion of parents and non-parents in their views.
• Other possible reasons might be discussed and investigated (difference in rural / urban population, subject got their license in New Zealand/overseas ( higher driving age in most countries etc.).

### Problem

Students pose a suitable comparison investigation question e.g. Is there a difference between parents with teenagers and other people in their opinion about a legal driving age of 18 or higher?

### Plan

Students devise a simple questionnaire, decide on sample size, collect data.

### Data

The data is cleaned, as necessary, and collated in a two-way table.

### Analysis

An initial exploratory data analysis is carried out. Proportions for parents (P) and non-parents (P’) are calculated and displayed in a simple histogram. The proportions might be p(P)=0.82, p(P’)=0.74. This results in a difference in the proportions p(P) - p(P’) of 0.08.

Software such as Fathom, Genstat, iNZight is used for bootstrap resampling to determine whether there is a difference in the population proportions. Bootstrap confidence intervals are found for the population proportions in each group. If these intervals overlap there may be no difference in the population proportions; the difference could have arisen from sampling variability alone.

### Conclusion

The conclusion is based on the findings from the analysis. Further factors can be discussed and further research can be suggested.

### Possible adaptations to the activity

• The amount of scaffolding will determine the difficulty of the activity. Other explanatory variables may be chosen. Other software (iNZight, Genstat) will be suitable.

• Media studies and geography are possible areas where students may be either collecting data or presenting data.

## Extension/enrichment ideas

•  In what situations is bootstrapping appropriate? What are the bases for relying on bootstrap intervals?

## Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standards:

## Spotlight on

### Pedagogy

• Encouraging reflective thought and action.
• Enhancing the relevance of new learning.
• Facilitating shared learning.
• Making connections to prior learning and experience.
• Teaching as inquiry.

### Key competencies

• Thinking:
• Students hypothesise, investigate, analyse and evaluate.
• Students design investigations, explore and use patterns and relationships in data and they predict and envision outcomes.
• Students ask questions, want to know ‘why’, make connections and discern if answers are reasonable.
• Students deal with uncertainty and variation, they seek patterns and generalisations.
• Relating to others:
• Students work in groups, they debate solutions, negotiate meaning and communicate thinking.
• Students work collaboratively and cooperatively, taking on a range of roles. They think, share ideas in pairs, and share ideas in groups.

### Values

Students will be encouraged to value:

• innovation, inquiry, and curiosity, by thinking critically, creatively, and reflectively.

### Māori/Pasifika

Engaging in discussion to improve health outcomes for Māori and Pasifika, for example, the link to the health and PE learning.