Back to the Kiwis…

The impact of sample size…Kiwi Kapers 2

Problem

I wonder what the median weight of New Zealand kiwis is?

Using technology…

Remember we’re in TEACHING WORLD - in the ‘real world’ we wouldn’t be able to take lots and lots of samples to see what happens!

Sampling kiwis Collecting the medians

from repeated sampling

Your collection of medians...

Analysis For each sample size:

A. I notice that the sample median weights of kiwis for samples of size ___ vary from ___ to ___

B. I notice that the bulk of the sample median weights of kiwis for samples of size ___ ranged from ___ to ___

C. I notice that the median for the sample median weight of kiwis for samples of size ___ is ___ and that the median for the sample IQR is ___

AnalysisSample size

I notice that the sample median weights of kiwis for samples of size ___ vary from ___ to ___

I notice that the bulk of the sample median weights of kiwis for samples of size ___ ranged from ___ to ___

I notice that the median for the sample median weight of kiwis for samples of size ___ is ___ and that the IQR for the sample medians is ___

n=15 from ___ to ___ from ___ to ___ Median-median = ___IQR-median = ___

n=30 from ___ to ___ from ___ to ___ Median-median = ___IQR-median = ___

n=50 from ___ to ___ from ___ to ___ Median-median = ___IQR-median = ___

n=100 from ___ to ___ from ___ to ___ Median-median = ___IQR-median = ___

Analysis

I notice that the variation of the median weights of kiwis ________ as the sample size _________.

For samples of size 15 the median weight ranged from ____ to ____, a difference of _____,

Whereas for samples of size 100 the median weight ranged from ____ to ____, a difference of ____.

Question?

What do you think will happen to variation in the IQR of the samples as we increase the sample size?

12kiwipopsample2IQR

ConclusionAs the sample size increases, • the variation of the medians __________• the variation of the IQRs _____________

What is a sensible and reliable sample size to use to make inferences about the population?

Conclusion

Remember Our best point estimate of the

population parameter – the population median is our sample median The estimates vary, even with n = 100 It is better to provide a range of possible

values for the parameter, based on our estimate, rather than stating one value

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Developing a reflex…

We want to plant a reflex…

Movies – one sample - summaryBox plot with memory…