Two means of small samples (n<30) – first we test if the standard deviations are the same so we can decide which t calculation to use.

Then we can do the hypothesis test to compare the means. In this case, the standard deviations were the same so we used the longer t formula with more degrees of freedom (n1+n2-2).

Two means of small dependent samples – we can find differences of pairs, and compute an average difference which might be zero, positive or negative.

Example continued

Two proportions – requires a “weighted estimate of population proportion” using both sample proportions, in order to compute a standard error for the sampling distribution.

Proportion example. Sorry this is so out of focus.

Example continued