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Meet the Kiwis…. Population of kiwis…. Species Weight (kg) Height (cm) Region/gender. Codes…. Species. Region. GS-Great Spotted, NIBr-NorthIsland Brown, Tok -Southern Tokoeka. NWN-North West Nelson, CW-Central Westland, EC-Eastern Canterbury StI -Stewart Island,
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Population of kiwis… Species Weight (kg) Height (cm) Region/gender
Codes… Species Region • GS-Great Spotted, • NIBr-NorthIslandBrown, • Tok-Southern Tokoeka • NWN-North West Nelson, • CW-Central Westland, • EC-Eastern Canterbury • StI-Stewart Island, • NF-North Fiordland, • SF-South Fiordland • N-Northland, • E-East North Island, • W-West North Island
Kiwi Kapers1 Take a handful of data cards and sort them Write some “I notice…” statements Look at what other people have done
Problem • I wonder what the median weight of New Zealand kiwis is?
I wonder what the median weight of New Zealand kiwis is? • What do you think the typical weight will be? • Why? • Sketch the shape of the distribution of weights of New Zealand kiwis.
Plan • What variable are we going to use to answer our question? • How are we going to gather our data? • Everyone? • Sample? • Simple random sample of 15 kiwis please.
Data • SRS of 15 kiwis • Make sure you don’t sample the same kiwi more than once
Analysis • Plot dot plot on axes • Add box plot above • Note the 5 point summary • {Minimum, lower quartile, median, upper quartile, maximum}
Analysis • Repeat three more times to complete 4 sets of 15 samples • Write (at least) three “I notice…” statements about your samples • Look at shape and spread – what do you notice? • Similarities? Differences? – between your sets of samples… • Make sure your statements include context • Would I be able to tell that you were looking at the weight of Kiwis?
Conclusion Use sample median to provide a point estimate of the population parameter • From my sample data I estimate that the median weight for all New Zealand kiwis is….
Conclusion • But they’re all different! • Who is right? • From my sample data I estimate that the median weight for all Stage 1 statistics students is….
Kiwi Kapers 1 Activity recaps… Language needed (eg population, sample, variables, etc) PPDAC cycle Question types Posing good investigative questions Sampling issues dot plot box plot Describing distributions
Kiwi Kapers 1 What do you think the population distribution will look like? *most values are between ___ & ___ * the largest value is about ___ * the smallest value is about ___ * the middle is around ___
Movies – one sample - summary Box plot with memory… n = 30 Sketch what you think the box plots with memory would look like for n = 10 n = 100 n = 1000 • ..\..\Pip\Animations_WILD\boxes_1samp_mem_30.pdf
Movies – one sample - summary Box plot with memory…
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 10
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 10
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 30
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 30
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 100
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 100
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 300
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 300
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 1000
Movies – one sample - comparison Box plots with memory… Could you make a call back in the population? n = 1000
Sample size vs making the call… If the samples are larger, the difference between the two groups doesn’t have to be as big to make the call that there is a difference between them BACK IN THE POPULATION L6 Guide – incorporates aspects of both spread and sample size
Kiwi Kapers 2 Explores what sample size we want to take to be reasonably sure that the inference(s) we make are representative of the population. I wonder what are typical weights of kiwis? What is a sensible and reliable sample size to use for making inference about a population
Go play on Fathom… … head down to the computer lab with your Kiwi Kapers 2 student fathom document…
TASK 1 – reflection What appears to be the effect of increasing the sample size on: the median from sample to sample? the IQR from sample to sample? the range from sample to sample?
TASK 2 – reflection What is a sensible and reliable sample size to use to make inferences about a population? • Samples of 30 or 50 are ok • Samples of 15 are too variable • Samples of 100, while even better, are not so much better that we need to spend the extra time and energy (and $) collecting 100 kiwis when 30 or 50 will do • We want the smallest sample that should give us a reliable estimate of the population
Kiwi Kapers 3 Develops students’ understanding of the L7 guide & informal interval estimates Under development
Kiwi Kapers 3 Under development Kiwi population
Kiwi Kapers 3 Under development Sample medians n = 30
Kiwi Kapers 3 Under development Sample medians n = 400
Kiwi Kapers 3 Under development Together population n=30 n=400 … ideas of how to put an interval estimate around our point estimate … is one IQR enough? … impact of sample size?
Lead into L7 guideline for informal interval estimate They cover the true population median approximately 9 out of 10 samples taken (shown with simulations)
Lead into L7 guideline for informal interval estimate Making the call at L7
