--- title: "Investigating with samples" subtitle: "Data and chance · Samples · Lesson 20" --- # Investigating with samples **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** 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? :::teacher-note **In one sentence:** 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). **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **A random sample of 40 students has a mean sleep of 8.8 hours. What can you say about all the students at the school?** ☐ Nothing at all ☐ Their mean is about 8.8 hours, give or take a little ☐ Their mean is exactly 8.8 hours My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** About 8.8 hours, give or take a little. A random sample of 40 gives a fair estimate, not the exact value. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Fair, ethical, honest :::keep-together ### Ethics Here is the routine for an inference. 1. $\text{Random sample of } 50 \text{ Year 9s at our school}$ — The sample and how it was chosen. 2. $\text{Median screen time } 3 \text{ hours, range } 6 \text{ hours}$ — What the sample shows. 3. $\text{Year 9s at our school: about } 3 \text{ hours}$ — Infer about the population sampled only. 4. $\text{A sample of 50 can be a little off; more students would narrow it}$ — State the uncertainty. **Which is the most important ethical step in a survey about students' sleep?** ☐ Teachers read the answers aloud ☐ Every student must answer ☐ Students agree to take part and their answers are kept anonymous ☐ Names are written on each form ::: :::teacher-note **Answer:** Students agree to take part and their answers are kept anonymous Ethical data collection asks permission, keeps answers private, and does no harm. ::: :::keep-together ### Find the mistake **Zara reports her investigation. Click the line where her inference goes too far.** ``` 1 Zara takes a random sample of 40 students at her school and asks about phone use after lights out. 2 Her sample's median is 45 minutes, and the range is 120 minutes. 3 She concludes that teenagers across Australia use their phones for about 45 minutes after lights out. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: her sample came from one school, so she can infer about her school, not all Australian teenagers. ::: :::keep-together ### Saying how sure **Which sentence states the uncertainty best?** ☐ From a random sample of 40, students at our school probably sleep about 8.8 hours; a bigger sample would give a closer estimate ☐ Students sleep exactly 8.8 hours ☐ We are certain students sleep 8.8 hours ☐ Students sleep 8.8 hours, which proves they are tired ::: :::teacher-note **Answer:** From a random sample of 40, students at our school probably sleep about 8.8 hours; a bigger sample would give a closer estimate Name the sample, use 'about' or 'probably', and say how the estimate could improve. ::: :::typical ## Plan and improve **Order the stages.** **A bigger sample.** **Anonymous answers.** **Which is more reliable.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Investigations :::keep-together ### One school **A random sample of 30 Year 10 students at one school finds most want a later start time. What can be inferred?** ☐ Nothing ☐ Most Year 10s at that school probably want a later start ☐ Most students in Australia want a later start ☐ Every Year 10 at the school wants a later start ::: :::teacher-note **Answer:** Most Year 10s at that school probably want a later start Infer about the population sampled: Year 10 at that school. ::: :::keep-together ### A fair question **Which question is fair to ask in an anonymous survey about exercise?** ☐ Why are you so lazy? ☐ Don't you think you should exercise more? ☐ What is your name and weight? ☐ How many minutes did you exercise yesterday? ::: :::teacher-note **Answer:** How many minutes did you exercise yesterday? Neutral, specific and respectful questions give honest data. ::: :::keep-together ### More certain **How can an investigation make its inference more certain?** ☐ Round the answer ☐ Use a convenience sample ☐ Ask only friends ☐ Use a bigger random sample ::: :::teacher-note **Answer:** Use a bigger random sample Bigger fair samples vary less, so the estimate is more certain. ::: :::keep-together ### Review: variation **Review: two random samples of 25 from the same school give means of 8.6 and 9.0 hours. What explains the difference?** ☐ A measuring mistake ☐ Sampling variation ☐ One sample was biased ☐ The school changed ::: :::teacher-note **Answer:** Sampling variation Random samples hold different students, so their means differ a little. ::: ## Make: 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. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A random sample of 50 students at your school shows a median of 2 hours of screen time on school nights. Write an inference with its uncertainty.** {{lines-3}} ::: :::teacher-note **Answer:** Students at our school probably have about 2 hours of screen time on school nights, from a random sample of 50; another sample might give a slightly different value. :::