113i - Planning a Statistical Investigation

Lesson 113 — Planning a Statistical Investigation

Strand: Statistics | Descriptor: AC9M8ST04 | Duration: 45 minutes

Block note. Lessons 113–118 form one connected investigation project: pose and plan the question (113), select an ethical and fair sampling method (114), collect and organise data (115), make inferences about the population (116), report findings while acknowledging uncertainty (117), and present and consolidate (118). Students keep a single project folder throughout.

Our class investigation question: What proportion of Year 8 students at our school meet the recommended daily screen-time guideline? — no more than hours of recreational screen time on a school day, per the Australian -Hour Movement Guidelines for children and young people. Population: all Year 8 students at our school, across classes of .

Learning Intentions

• To understand the plan stage of a statistical investigation involving a population proportion.
• To write a statistical question that asks about a proportion, with a precisely defined variable.

Success Criteria

I can:

1. Name and describe the five stages of a statistical investigation.
2. Distinguish a proportion question (“what fraction meet a condition?”) from a mean question (“what is the typical value?”).
3. Define the population, sample and variable for our class investigation, with a precise operational definition.
4. Write a testable prediction for the investigation.

Warmup

(5 minutes — proportion or mean? pairs)

Sort each question as asking for a proportion (what fraction/percentage meet a condition) or a mean (what is the typical value).

1. What percentage of Year 8 students walk to school?
2. What is the average number of siblings Year 8 students have?
3. What proportion of households in the suburb recycle every week?
4. How many hours of sleep does a typical Year 8 student get?
5. What fraction of a sports team’s shots are successful?

Answers: 1. Proportion; 2. Mean; 3. Proportion; 4. Mean; 5. Proportion.

The distinction that matters today: a proportion question needs a variable with only two categories (meets the condition, or does not) — everyone in the sample is sorted into one bucket or the other, then we report what fraction landed in the “yes” bucket. This is the question type behind today’s investigation, and behind Lessons 111–112’s sample-size work.

Activities

Activity 1 — Explicit Instruction: Planning a Proportion Investigation (13 min)

The five stages of a statistical investigation:

Stage	What happens	Key question
Pose	Write a statistical question about a proportion; define the variable, population and sample	What exactly am I asking, and about whom?
Plan	Choose a fair, ethical sampling method (Lesson 114)	How will I select a sample that fairly represents the population?
Collect	Gather and organise the data accurately (Lesson 115)	Is my data trustworthy and well organised?
Infer	Use the sample proportion to draw a conclusion about the population (Lesson 116)	What can I honestly conclude about everyone, from data on a few?
Report	Communicate findings, acknowledging uncertainty (Lesson 117)	How confident can I be, and how do I say so honestly?

A good proportion question has four properties, mirroring what makes any statistical question strong:

1. It names a measurable condition with a clear yes/no test.
2. It specifies a population.
3. It anticipates that the sample will not perfectly match the population (this is why we need Lessons 111–112’s ideas).
4. It is answerable with data collectable in the time available.

I do — testing our class question against the four properties:

“What proportion of Year 8 students at our school meet the recommended daily screen-time guideline?”

• Measurable condition: ” hours of recreational screen time on a school day” — but this needs a precise operational definition (see below).
• Population: all Year 8 students at our school.
• Anticipates sample variation: yes — different samples of Year 8 students will likely give somewhat different proportions, which is exactly what Lessons 111–112 predict.
• Answerable: yes, with an anonymous survey, within one lesson.

Defining the variable precisely — the step students most often skip.

Weak: “Do you use screens too much?”

• Not measurable — “too much” is an opinion, not a test.

Better: “On a typical school day, do you spend hours or less on recreational screen use (games, social media, video, non-homework browsing) — yes or no?”

• Names a threshold, a time frame, and explicitly excludes homework/study screen time, which is not part of the guideline.

We do — sharpen these weak proportion questions together:

1. “Do most students eat breakfast?”
2. “Are Year 8 students getting enough sleep?”
3. “Do students recycle?”

(Sample improvements: “What proportion of Year 8 students eat breakfast on a typical school morning?”; “What proportion of Year 8 students get at least hours of sleep on a school night?”; “What proportion of Year 8 households place a recycling bin out every fortnight?“)

Activity 2 — Write the Investigation Plan (15 min)

Pairs. This plan is carried into Lesson 114, where the sampling method is finalised.

Your task. Using the class investigation question above (or, if directed by your teacher, a related proportion question about student habits), write a plan covering all six points:

1. The question — copy it precisely, including the threshold.
2. The variable — the exact yes/no test you will use, written so precisely that two different people asking the same student would always record the same answer.
3. Population — who the investigation is really about.
4. Sample (draft) — roughly how many students, and from where; you will refine this method in Lesson 114.
5. Collection method (draft) — how each student will be asked, and how anonymity will be protected.
6. Prediction — your estimate of the population proportion, and your reasoning.

Circulating prompts:

Prompt	Purpose
Would two different people asking the same student always get the same answer?	Forces a precise, testable variable definition.
Is “recreational” screen time clearly separated from “homework” screen time in your wording?	The commonest source of inconsistent answers in this investigation.
What is your population, and is your planned sample really drawn from it?	Population-versus-sample honesty, carried from Lesson 106.
What result would make your prediction wrong?	Makes the prediction testable, not decorative.
Could this be collected, anonymously, in one lesson?	Practicality check.

Activity 3 — Inquiry: Stress-testing the Question (7 min)

Pairs swap plans.

Read another pair’s plan and answer:

1. Could you apply their yes/no test to yourself right now, without asking a clarifying question?
2. Is there any wording in their question that could be read two different ways?
3. Is their population clearly stated, and does their planned sample look like it could fairly represent it?

Then: each pair revises their variable definition in response to one comment received, and notes the revision.

Checks for Understanding

(5 minutes — exit ticket, collected with the plan)

1. What is the difference between a proportion question and a mean question? Give one example of each.
2. Name the five stages of a statistical investigation.
3. State the population and the variable for our class investigation.
4. Rewrite as a precise proportion question: “Do students exercise enough?”
5. Reasoning. Explain why the variable “recreational screen time hours” needs a precise definition of what counts as “recreational”, using an example of an ambiguous case (e.g. watching an educational video).

Answers: 1. A proportion question asks what fraction meets a yes/no condition (e.g. “what proportion of students walk to school?”); a mean question asks for a typical value (e.g. “what is the average time students take to get to school?”); 2. Pose, plan, collect, infer, report; 3. Population: all Year 8 students at our school; variable: whether a student spends hours per school day on recreational screen use (yes/no); 4. E.g. “What proportion of Year 8 students at our school get at least minutes of physical activity on a typical school day?”; 5. Without a clear rule, some students might count an educational video as “recreational” and others as “not screen time at all”, producing inconsistent data that cannot be fairly compared or combined — the investigation needs one shared rule applied the same way to everyone.

Common Misconceptions

Misconception	How to pre-empt it
Treating a proportion question as if it were a mean question (e.g. trying to find an “average” of yes/no answers).	The warmup’s explicit sort, and Activity 1’s four-property check.
Leaving the variable’s threshold or scope vague (“screen time” without a time frame or category).	The two-different-people test in the circulating prompts.
Believing the sample must match the population exactly for the investigation to work.	Explicitly connect to Lessons 111–112: some mismatch is expected, and is what “uncertainty” (Lesson 117) will describe.
Writing a prediction with no reasoning attached.	Point 6 of the plan requires “and your reasoning”.
Confusing the sample with the population when stating who the investigation is “about”.	Population and sample listed as separate, required points.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). Which of these is a proportion question: “What is the average screen time of Year 8 students?” or “What percentage of Year 8 students exceed hours of screen time?”

Answer

The second — it sorts students into two categories (exceeds / does not exceed) and asks for the fraction in one category. The first asks for a typical numeric value, which is a mean question.

E2 (AMC Junior style). A question reads: “Do you think you use screens responsibly?” Name the flaw and rewrite it as a measurable proportion question.

Answer

It asks for an opinion, not a measurable fact — “responsibly” is not testable. Rewrite: “On a typical school day, is your recreational screen time hours or less — yes or no?”

E3 (Challenge). A student plans to ask: “Do you spend a lot of time on your phone?” Explain two different students could honestly answer this question differently despite having identical screen-time habits.

Answer

“A lot” is subjective — one student might consider hour “a lot” if their friends use less, while another with the same hour might consider it normal. Without a fixed numeric threshold, the same behaviour produces different answers depending on each student’s personal sense of scale.

E4 (Challenge). The class investigation defines the population as “all Year 8 students at our school”. A pair proposes surveying only their own class of . Explain what this changes about the investigation’s scope.

Answer

Their class of becomes the sample, and the population remains all Year 8 students — but a single class may not fairly represent the other six classes (Lesson 114’s concern). If they instead intend to draw conclusions only about their own class, the population itself would need to be redefined as “students in this class”, which is a different, much smaller investigation.

Homework

1. Explain in one sentence what makes a question a proportion question rather than a mean question.
2. Rewrite each as a precise proportion question: (a) “Are students happy with the canteen?” (b) “Do people get enough sleep?” (c) “Are Year 8 students active?”
3. For your Q2(c) question, write a precise, testable definition of “active” that two different surveyors would apply identically.
4. Name the five stages of a statistical investigation and write one sentence on each.
5. State one reason a proportion investigation’s sample might not exactly match the population’s true proportion, referring to ideas from Lessons 111–112.
6. Write a prediction for the class screen-time investigation, with a reason based on what you already know about Year 8 students’ habits.
7. Reasoning. Explain the difference between “population” and “sample” using the class investigation as your example.
8. Reasoning. A friend says a good statistical question should have “a definite right answer everyone would agree on”. Explain what is right and what is missing from this description, using the idea of variability.
9. Challenge. Design a full proportion-question plan (question, variable definition, population, draft sample, draft collection method, prediction) to investigate: “What proportion of Year 8 students bring a reusable water bottle to school?”

Answers: Q2 — e.g. (a) “What proportion of students rate the canteen or out of ?” (b) “What proportion of Year 8 students get at least hours of sleep on a school night?” (c) “What proportion of Year 8 students get at least minutes of physical activity on a typical day?” Q3 — e.g. “counts as active if they report at least minutes of moderate-to-vigorous movement (sport, walking, cycling, active play) on that day — yes or no.” Q5 — because each sample is only a subset of the population, and different subsets can by chance include slightly different proportions of students who meet the condition, exactly as seen when comparing same-size samples in Lessons 111–112. Q7 — the population is everyone the investigation is really about (all Year 8 students); the sample is the smaller group we actually collect data from and use to estimate the population’s proportion. Q8 — right: the variable itself should be measurable and testable, so any two people applying the definition get the same classification for a given student; missing: a good statistical question does not have one definite answer for the group as a whole — it anticipates that different individuals (or different samples) will vary, which is exactly what makes it worth investigating with data. Q9 — student’s own; must include a precise “reusable bottle brought that day” test, population of students, a sample size and rough method (e.g. random selection across all seven classes), a collection plan preserving anonymity, and a reasoned prediction.