These are study designs for testing whether one condition produces a greater value on average than another condition.
Assuming conditions A and B, for each observation for A, there is a corresponding observation for B. Example: in assignment 8, each price for vender A has a corresponding price for vender B since you check prices for the same article.
For a paired-difference design, a statistical test will calculate the differences among the pairings. This produces one sample of values. The analysis then tests if the mean of the sample is not zero.
This design is covered in section 7.1 of the text.
This design collects one sample under the first condition and another sample under the second condition. There are no pairings across the conditions. Example: It has been rumoured that the LCD panels coming from company A have more dead pixels than the panels coming from company B. To test this hypothesis, a sample of 20 panels are tested from each company. The text calls these problems "two-sample" problems and discusses them in section 7.2.
T-tests are typically used for both designs. For the paired-difference design, the t-test assumes that the paired-differences fit a normal distribution. For the independent samples design, the t-test assumes that the data in each sample fit a normal distribution.