A lathe is a machining tool that spins a piece of material for shaping, and operators usually have a significant effect on the output of a lathe. Suppose that we want to test the quality of output of a new lathe against the quality of output of an old one. We have 10 operators each use each lathe and then compare their outputs to each other according to industrial standards, using a matched pair design. What would the blocks be?

In the context of evaluating a new and old lathe using a matched pair design, the operators serve as blocks to control for variability due to skill levels. Each operator tests both lathes, ensuring a fair and reliable comparison.

In evaluating the quality of output from a new lathe versus an old lathe using a matched pair design, we need to determine the blocks in this experimental setup.

A block refers to a grouping of experimental units that are similar in ways that are expected to affect the response to the treatments. For this experiment, the blocks would be:

Operators: Each of the 10 operators will serve as a block. This is because the operators' skill levels can potentially influence the output quality and introduce variability in the results. By using each operator as a block, we control for this variability.
Lathes: Both the new and old lathes are tested, and their outputs are compared for each operator. Here, each lathe's performance is considered for every block.

This setup ensures that the comparison of lathe performance is not confounded by differences in operator skill levels, thus providing a more accurate assessment of each lathe's capabilities.

Using a matched pair design offers several benefits:

Reduces variability due to operator skill differences.
Ensures a fair comparison between the two lathes.
Improves the reliability and validity of the results.