Experiments whose outcome measures are quantitative variables are often analyzed by comparing means. The Student's t-test is the most commonly used statistical test for comparing two means or for comparing an observed mean with a known value. If more than two groups are observed, an analysis of variance (ANOVA) is used to compare means across groups (discussed in Chapter 13).
A one-sample t-test is often used to compare an observed mean with a known or “gold standard” value. For example, in a quality control setting, you may be interested in comparing a sample of data to an expected outcome, such as the observed calories of liquid in cans of baby formula against the claim on the label. The purpose of the one-sample t-test, in this case, is to determine if there is enough evidence to dispute the claim. In general, for a one-sample t-test you obtain a random sample from some population and then compare the observed sample mean to some fixed value. The typical hypotheses for a one-sample t-test are as follows: