Year 12 Statistics workshop
contact: parnold@cognition.co.nz
Activity
Detail
Resources
Overview of unit
Achievement objectives, indicators and definitions from Senior Secondary Guides
Some notes at the end about our thinking - draft ideas!!
YEAR 12 STATISTICS.docx
Working with categorical data – sampling variability and sample size
Sampling errors - Variability of sample proportion
Political polls see Stats Chat
http://www.statschat.org.nz/2011/11/08/political-poll-with-sample-size-of-47-makes-headlines/
Using populations of counters to draw samples of size 20 and observe the variability in outcomes. (some notes in introduction to making an inference about a population Introduction to making an inference about a population.doc - by Neil, Rochelle and Lindsay)
to tag or not to tag http://www.censusatschool.org.nz/classroom-activities/to-tag-or-not-to-tag/
margin of error (stats teachers day 2006) Marina and Anne http://www.stat.auckland.ac.nz/~teachers/index6.php
Word document to support Poll of 47 activity.
POLLOF47.docx
Working with categorical data – sampling variability and sample size
Kiwi Kapers 1 http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AO-S7-1
Introducing sampling variability through repeated sampling from the same population using sample sizes 15 and 30. Looking for patterns across repeated samples of the same size.
  • Five samples of size 30 for each pair/group of students (keep a record of these 5 sample medians for Kiwi Kapers 3)
  • 5 samples of 15 and 5 samples of 30 needed for Kiwi Kapers 2
kiwi kapers data cards
weight sample sheets
sellotape or blu tac
whiteboard markers blue and red

Kiwi Kapers 2 http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AO-S7-1
Exploring different sample sizes and mutually agreeing to a sensible size based on smaller variation of sample medians combined with practical considerations such as the efficient use of time and resources. (Catching kiwis to collect the data)
This activity is built around using Fathom to generate multiple samples, but this could easily be done using the data viewer http://www.censusatschool.org.nz/2010/data-viewer/ on CensusAtSchool to collect sample medians for samples of size 50 and 100. (Sample medians for sample size 15 and 30 can be used from the Kiwi Kapers 1 activity).
  • Under PLAN select the Kiwi Kapers 2008 population and select total sample size of 50 and then 100 (ignore the “I am a year 12 student” at this stage).
  • Select get my sample (this provides a sample which shows in DATA).
  • Under ANALYSIS, select variable 1 as weight and then tick “Add summaries”. Now click “Do Analysis”. Record median.
  • Click back in the sample size box and hit enter – generates a new sample.
  • Repeat ANALYSIS, select variable 1 as weight and then tick “Add summaries”. Now click “Do Analysis”. Record median.
  • Continue until X sample medians have been found.
  • Collate class results.

Making inferences in summary situations
Kiwi kapers 3
Follows Kiwi Kapers 2. This activity is split into two parts. Collectively they aim to develop the method for finding informal confidence intervals for medians.

In part one students develop the concept of dividing the sample IQR by Ön, recognising the effect of sample on the variability of an estimate.

In part two students discover the width of the informal confidence intervals such that the informal confidence intervals capture the population median about 90% of the time.
Teaching notes
kiwikapers3teachernotes.doc (updated 10 March, still might have tweaks to the conclusion by Pip and Jeanette)

excel spreadsheet with 1000 sample informal confidence intervals calculated
intervaltest1000samplessize30.xlsx

spreadsheet including median and IQR for each sample, first 20 or so highlighted
1000sampleswithIQR.xlsx

Student worksheets
Part 1
kiwikapers3studentworksheetv2.doc (updated 10 March)
Part 2
kiwikapers3studentworksheetPART2.doc (updated 10 March)
Using PPDAC cycle
Two activities developed to use the PPDAC cycle with their new knowledge, but the activities also have in particular sampling flaws in them. they are designed to support the lead into the next section on sampling.

Tuck shop
Explores amount of money spent on lunch
sleep hours
Explores amount of sleep for teenagers
http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10399080
http://liveto100.everybody.co.nz/sleep/how-much-sleep-is-enough
PPDACpracticeL7summary.docx worksheet needing own data collected in school (by Sophie)

PPDACpracticeL7summarywithdata.docx worksheets with data provided (actual data collected from a school tuck shop and from year 12 class)

one in five teenagers not getting enough sleep
One in five teenagers not getting enough sleep.docx
copy of herald article
heraldsleeparticle.docx
how much sleep recommendations
How much sleep is enough.docx
Sampling
Sampling stuff 1 http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AO-S7-1

Sampling stuff 2 http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AO-S7-1
kiwi kapers data cards
height graphs
Making inferences in comparison situations
Does the median height of female kiwis tend to be greater than the median height of male kiwis? - this was not a good question to explore as the boxes don't overlap. some work needed here to find questions and data that require the students to find the informal confidence interval because both of the medians are inside the overlap.

Make the call if the informal confidence intervals don't overlap.

Maybe exploring sleep times of boys and girls.