A sample investigation asks a question about a population, plans a fair and ethical sample, collects and describes the data, then makes an inference about the population and says how sure it can be.
You can't see the whole school's answer, only your sample's. How close is your estimate, and how would you say so honestly?
In real investigations you only see your sample. An inference is a conclusion about the population drawn from a sample.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
What can you say?
TryTry it on the board and compare the result with your prediction.
Infer, then check
A good inference:
is about the population the sample came from
gives an estimate, not an exact value ("about")
says how sure you can be, and why (the sample's size and how it was chosen)
Try it yourselfYour edits are saved in this browser.
The school's mean is hidden. Take a fair sample (not convenience), write your estimate of the school's mean sleep, then press Show the population. How close were you? Compare with your prediction.
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Fair, ethical, honest
Here is the routine for an inference.
Worked exampleBefore each step, say what you think comes next.
Random sample of 50 Year 9s at our schoolThe sample and how it was chosen.
Median screen time 3 hours, range 6 hoursWhat the sample shows.
Year 9s at our school: about 3 hoursInfer about the population sampled only.
A sample of 50 can be a little off; more students would narrow itState the uncertainty.
Read Zara's conclusion. Who was in her sample?
Zara reports her investigation. Click the line where her inference goes too far.
ModifyChange the problem on purpose and see what happens.
Plan and improve
Need a hint?
Take a sample of 20 and one of 80 or more before you reveal the population.
Try it yourselfYour edits are saved in this browser.
Put the stages of the investigation in order.
Pieces (click to add)
Your program
Estimate the proportion of students who play sport from a random sample of 80 or more, then show the population. Was it closer than a sample of 20 usually is?
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Investigations
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Plan your investigation
Choose a question about your school (sleep, screen time, travel to school, lunch). Write the plan as five stages. If your teacher agrees, carry it out with a class sample and write the report.
Need a hint?
Name the population first, then the sampling method and size.
Another hint
Include how you will ask permission and keep answers private, and how you will say how sure you are.
For teachers
Students estimate a hidden population value from samples, then plan an ethical sample investigation and state an inference with its uncertainty (AC9M8ST04, nodes 1 and 2). About 45 minutes.
I can plan an investigation with a fair, ethical sample.
I can make an inference about a population from a sample.
I can say how sure I am, and why.
Before class
Do the Run board yourself first. Students need sampling methods, describing samples and sampling variation (the last three lessons), and the Year 7 investigation cycle.
The one idea: an inference estimates the population that was sampled, with its uncertainty stated (size and method). The common mistake is inferring beyond the population (Zara's one school to all Australian teenagers).
The board hides the school's value until Show the population, so students commit to an estimate first. Ethics: consent, anonymity, no harm, and neutral questions; school approval for real surveys.
The full investigation (collecting real data) is a class task: the Make step plans it. Use a class sample of a short anonymous form on a non-sensitive topic.
Running the lesson
Predict: ask what 'give or take' would mean here.
Run: ask for the estimate before the reveal.
Investigate: ask Zara who her sample can speak for.
Modify: ask why the bigger sample's estimate is safer.
Make: ask how you will protect the people who answer.
The hard part (on purpose)
Saying how sure you are without overclaiming. Ask: who exactly does this sample speak for, and how close might it be?
When students get stuck
A student writes an exact value for the population. Ask: Did you measure everyone? Fix: Use 'about' or 'probably', and give the sample.
A student generalises to a bigger group. Ask: Who could have been chosen for this sample? Fix: Only that population: the school, the year, the club.
A student forgets ethics in the plan. Ask: How will people agree to take part, and stay anonymous? Fix: Add consent, anonymity and a neutral question to the plan.
Stretch and support
Stretch: Run your investigation twice with two different random samples. How different are the results, and what does that say about your uncertainty?
Support: A five-stage plan template: question, sample, collect (ethically), display and describe, infer with uncertainty.
Where it leads
This completes AC9M8ST04 and Year 8 Statistics.
Where it leads: Year 9 and 10 statistics (comparing samples, scatterplots, evaluating claims in the media).
What each step is for
what can you say?: Committing to what a sample's mean says about the school shows whether they think in estimates.
infer, then check: Estimating from a sample with the population hidden, then revealing it, shows how close a fair sample's inference is.
fair, ethical, honest: Ethics protects the people in the sample; an inference stays inside the population sampled (Zara); uncertainty is stated, not hidden.
plan and improve: Ordering the stages, and seeing that a bigger sample tightens the estimate, prepares them to plan their own.
investigations: Choosing populations, ethical methods and honest inferences, mixed; inferring beyond the sampled population is the planted slip; sampling variation is the review.
plan your investigation: Planning a full sample investigation, with ethics and uncertainty, shows they can apply every part of the unit.
Now you can
Plan an investigation with a fair, ethical sample.
Make an inference about a population from a sample.