Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

One-Sample t-Test

A one-sample t-test has to be applied in order to compare the mean of a sample to a predefined target value. It is assumed that the target value is known (or defined) in advance.

A typical situation where a one-sample t-test would be applied could be as follows: a pain-relieving medicine used in a hospital brings relief to the patients within 130 seconds (this number is known from thousands of applications in the past). When introducing a new drug, it is administered to 30 patients and the time until the pain reliever shows an effect is recorded. The mean time until relief is 112 seconds with a standard deviation of 43 seconds. Is there any evidence that the new drug reduces the time until a patient receives relief from pain?

In this example we have to test a sample mean (the mean relief time for 30 patients) against a predefined limit. Note that the limit is fixed and well-known. If the limit were not predefined but obtained from another sample (i.e. another 30 patients receiving the old drug), we would have to apply a two-sample test.