Final answer:
The appropriate design is a test of matched pairs, suitable for assessing the significance of the weight changes before and after the diet in the same group of volunteers.
Step-by-step explanation:
The appropriate design for testing the significance of the difference between the means of the eighteen overweight volunteers' weights before and after a two-week diet is a test of matched pairs. This is because the same subjects are measured twice, once before the diet and once after. When dealing with repeated measurements on the same subjects, the matched-pairs t-test (also known as the paired samples t-test or the dependent samples t-test) is used to determine if there is a statistically significant difference between the two sets of observations.
The null hypothesis (H0) in this case is typically that there is no difference in the mean weights before and after the diet, while the alternative hypothesis (Ha) would be that there is a difference in the means.