Thoughts on Teaching Week 6 tutorial
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Thoughts on Sect. 6.3
Encourage drawing diagrams! A common error: plugging numbers into calculators wrongly, and effectively computing \(z = x - (\mu/\sigma)\) rather than \(z = (x - \mu)/\sigma\).
Notice that students cannot be very accurate using the \(68\)--\(95\)--\(99.7\) rule, which is one of the points to be made: only a guess can be made, but using \(z\)-scores leads to more accurate answers.
You could have a discussion about rounding.
Is it sensible to quote to the nearest millimetre, or tenth of a millimetre?
Thoughts on Sect. 6.6
Since samples are easy to generate, you can have each group/person in class generate a few simulations. On the whiteboard, you can tally these, and produce a histogram. Obviously, the more sets of \(10\) you can generate, the better... and the webpage is fast... but don't take too long doing so.
One purpose is to show students about sampling variation: not every set of \(10\) tosses produces the same value. The main purpose is to demonstrate what we mean by a sampling distribution: the distribution that shows how a sample statistic varies from sample to sample. After drawing the histogram from your classes data, you may wish to point out where certain groups' \(\hat{p}\) values are located.