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The Independent Samples T Test compares the mean scores of two groups on a given variable.
You use a z test when you are testing a hypothesis that is using proportions You use a t test when you are testing a hypothesis that is using means
You could use a two-tailed t-test. You would use a two-tailed test instead of a one-tailed test because you are not hypothesizing which direction the difference will be. If you hypothesize before hand the direction of change, you could use a one-tailed test.
It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.
The"t" test, (called the "small 't' test, to distinguish it from the large 'T' test) is a test for deviation from a known norm, using a smaller sample set than the one required by the large T test. It is said to have been developed by the head of quality control at the Guinness Brewery in Ireland.