1. a paired test would be used when the two populations consist of match pairs of related data. For example, glucose levels in patients' blood before a medication and after. Or, matching observed data (e.g. actual glucose levels) with predicted data (expected glucose levels.)

2. You would use a two population test with independent populations when comparing two different groups. For example, comparing the mathematical ability of males and females at a school. Or, comparing the productivity of one data entry team to another data entry team in the office.

H0: group 1 sample mean (i cannot type the mu symbol here)-group 2 sample mean = 0

H1: group 2 sample mean (i cannot type the mu symbol here)-group 2 sample mean "does not equal"(again, should by symbol, but can't type here) 0.

see your text book for formulas with the proper symbols I could not type.

In a one tailed test, you just want to know if a sample mean is greater than the population mean. OR, if the sample is less than the population mean. If you want to know if the mean is off in either direction in the same study, you would use a two tailed test. For example, if you want to know if the sample temperatures were higher than the population mean, you would use a one tailed test. If you want to know if the sample temperatures were higher OR lower than the population mean, then you would use a two-tailed test.