Week 5 lecture
Postscript to Week 5 lecture
When using a 95% confidence interval or a zstatistic compared to a 'critical value' of 1.96:

It is NOT the case that 95% of the time that you will draw the right conclusion about a suggested value for the population mean (which is what I was tempted to say in the lecture!)

It IS the case that 95% of the time that you will draw the right conclusion about a suggested value for the population mean if the suggested value is correct.

In other words, it is unlikely that the suggested value for the population mean is correct but is rejected as being implausible, because this would mean that the amount of sampling error (i.e. the difference between the sample mean and the population mean) fell into the 5% of largest quantities of sampling error.