## Thoughts on Teaching Week 6 tutorial

### 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.