There are various types of t-tests. The following are the most common one. They typically formulate a null hypothesis that makes a claim about the mean of a distribution:

• One-sample independent t-test: This is used to compare the mean of a sample with that of a known population mean or known value. Let's assume that we're health researchers in Australia who are concerned with the health of the aboriginal population and wish to ascertain whether babies born to low-income aboriginal mothers have lower birth weight than normal.

An example of a null hypothesis test for a one-sample t-test would be this: the mean birth weight for our sample of 150 deliveries of full-term, live babies from low-income aboriginal mothers is no different from the mean birth weight of babies in the general Australian population—that is, 3,367 grams.

The reference for this information can be found at http://www.healthinfonet.ecu.edu.au/health-facts/overviews/births-and-pregnancy-outcome.

• Independent samples t-tests: This is used to compare means from independent samples with each other. An example of an independent sample t-test would be a comparison of the fuel economy of automatic transmission versus manual transmission vehicles. This is what our real-world example will focus on.

The null hypothesis for the t-test would be this: there is no difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average combined city/highway mileage.

• Paired samples t-test: In a paired/dependent samples t-test, we take each data point in one sample and pair it with a data point in the other sample in a meaningful way. One way to do this would be to measure against the same sample at different points in time. An example of this would be to examine the efficacy of a slimming diet by comparing the weight of a sample of participants before and after the diet.

The null hypothesis, in this case, would be this: there is no difference between the mean weights of participants before and after going on the slimming diet, or more succinctly, the mean difference between paired observations is zero.

This information can be found at http://en.wikiversity.org/wiki/T-test.