ࡱ> a jbjb,, 7NNN@: nnnnB84RtBwL(>+ KKKKKKK,KNRPvL777L}nn1L}}}7nK}$,nnnn7K}}GDvhJ ?{7FH&JGL0wL IQ}QLJ}BBBBTitle: Ready, Steady, Go Achievement Objectives: S6-1C Identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays S6-1D Making informal inferences about populations from sample data S6-1E Justifying findings, using displays and measures S6-1A Justifying the variables and measures used Key Competencies: Thinking: Engage in sense making Deal with uncertainty and variation Make predictions Seek patterns and generalisationsThis activity explores the following key ideas: Comparing samples Making inferences about populations Resources Worksheets for groups OHT and pen for each group Teacher access to internet in classroomPrior Knowledge: Sample Construction and analysis of dot plots and box plots Adapting for ICT Students present graphs and conclusions electronically using data projector or using graphics calculator and view screen Introduction/Background The focus of this lesson is on comparing two samples and making an inference about populations from samples. Students previous work on box plots and work on sampling ideas are combined in this activity. Discuss in what situations reaction times are important. (E.g. driving. Winter Olympics, Commonwealth games, sports, safety) Students analyse samples in groups. Each group has different samples. Groups report back with OHT of own graphs and conclusions. Teacher uses CensusAtSchool online to demonstrate effect of larger samples on inferences and to show population distribution. Problem Do Year 10 students have faster reaction times than Year 5 students? Plan Explain how the CensusAtSchool survey measured reaction time. Students clicked a button on the screen and then waited for it to change colour, at which stage the students reacted and clicked the button as fast as they could. The computer then automatically recorded their reaction time. The reaction time was a measure of the delay between the change of colour and when the student clicked the button. Note that some students did no understand the question or were very inattentive and recorded more than 4 seconds. Therefore such data were recorded as 4 seconds. (Normally students would be given practice runs). Demonstrate online (either student or teacher) go to  HYPERLINK "http://www.censusatschool.org.nz/2007/questions/" www.censusatschool.org.nz/2007/questions/ scroll down to question 13; follow instructions. Discuss whether they think the reactions times for Year 10 and Year 5 students will be different or the same. Ask students to draw their prediction of the shapes of the reaction time distributions for all students in Year 10 and in Year 5 and write down why they choose a particular shape. Shapes could be dot plots or histograms. [This could be done on strips of paper and displayed for later reference]. Data  From the CensusAtSchool database each student group (2-3 students) will be given samples of the same size (n=20) from two populations, Year 5 and Year 10. Each group will have different samples. Be aware of the likely student misconception that samples must be same size for valid comparisons. Analysis  Students draw dot plots and box plots. When they analyse the data to answer the question, they should write I notice statements to Compare sample statistics (means, medians, quartiles) Compare shapes of graphs Compare spreads (IQR) Compare middle 50% of data Transfer graphs and conclusions to OHT for sharing with class. Conclusion When students make a conclusion, they should: Answer the question e.g. based on evidence from the data, it seems Quantify the answer; quote numerical values of statistics and compare graphs Generalise the answer (make an inference) to reaction times of all NZ students in Years 5 and 10 Groups will compare their boxplots using OHTs and conclusions. Discuss whether each group arrived at the same conclusion. Discuss when they might be prepared to make a decision that the populations are different. What are some possible criteria for making such a decision? Remind them about sampling variability. Let class suggest you draw larger samples to compare. Compare shapes, centres and spreads of graphs. Using the Random Sampler on the CensusAtSchool website draw several samples of different samples sizes and compare box plots. Go to  HYPERLINK "http://www.censusatshchool.org.nz/2007/classroomactivities/ready-steady/" http://www.censusatshchool.org.nz/2007/classroomactivities/ready-steady/ Click on sample Click on Get Sample data button Click on Box Whisker Viewer (for online graphs) Check comparison and graph type, choose box and whisker with data points. Check sample size (10, 20, 30, 40 or 50) Click resample Finally draw the populations and compare. Go back 3 pages and click on entire population. Compare conclusions derived from samples with the comparison of the actual populations. Reflection To what extent have key ideas been learned? Where to from here? 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