Wasteoftime

For

(point of estimation of the population mean) +/- (reliability factor t-stat) X (standard of error) ;use this when the Qn ask for Confidence interval. The reliability factor is also the "critical value" (Read from the table) For the <standard of error> you can imagine it to be Standard deviation in your bell curve.

And for

(sample mean - hypothsized mean)/ (standard of error) ;
this is to find the z/t statistic of which you will compare it with the critical value and decide (depending if its two-tailed or one-tailed) if to reject null hypothesis.
To use t statistic, when population variance is unknown and you have small sample size(n<30).
For z-statistic, you use when you the population variance is known. You can also use z-statistic, when the population variance is unknown and n>equal to 30. As large sample tends to the normal distribution.
For the above formulae, its a general one. Mean - given usually. hypothesized mean - mean you based your hypothesis on. and the standard error -> can be found using both pop standard deviation & sample standard deviation divide by the sq root of size n.

Hope it helps.