The following situations all require inference about a mean or means. Identify each as a single sample, matched pairs, or two independent samples.

a. An education researcher wants to learn whether inserting questions before or after introducing a new concept in an elementary school mathematics text is more effective. He prepares two text segments that teach the same concept, one with motivating questions before and the other with review questions after. Each text segment is used to teach a different group of children, and their scores on a test over the material are compared.

b. Another researcher approaches the same problem differently. She prepares two text segments on two unrelated topics. Each segment comes in two versions, one with questions before and the other with questions after. Each of a group of children is taught both topics, one (chosen at random) with questions before and the other with questions after. Each child’s test scores on the two topics are compared to see which topic he or she learned better.

c. To evaluate a new analytical method, a chemist obtains a reference specimen of known concentration from the National Institute of Standards and Technology. She then makes 20 measurements of the concentration of this specimen with the new method and checks for bias by comparing the mean result with the known concentration.