Final answer:
The statement that we first take the difference of each pair of observations and then do inference on these differences in a paired analysis is true. This is an essential step in hypothesis testing for matched or paired samples, involving dependent samples and the testing of the population mean of the differences.
Step-by-step explanation:
In a paired analysis, the statement that we first take the difference of each pair of observations and then do inference on these differences is true. This is a fundamental step in hypothesis testing for matched or paired samples. Specifically, when conducting a t-test for matched or paired samples:
- Two measurements (samples) are taken from the same pair of individuals or objects. This characteristic defines them as dependent samples.
- The differences between each paired set of measurements are calculated, forming a new sample of differences.
- The hypothesis test is then carried out on these calculated differences, not directly on the original measurements.
- The assumption for the sample of differences is that they come from a population with a normal distribution, or that the sample size is large enough for the distribution of the sample mean of differences to be approximately normal.
Therefore, answer choices B and C from the options given earlier are true: B. Two measurements are drawn from the same pair of individuals or objects, and C. Two sample means are compared to each other. The parameter tested is the population mean of the differences (xd).