What test should be used to determine if patients' average weight decreased after a specialty diet?

The paired t-test is the appropriate choice for determining if patients' average weight decreased after a specialty diet because it is specifically designed for situations where two related measurements are taken from the same subjects. In this case, the weights of the patients would be measured before and after the implementation of the specialty diet, creating a scenario where each individual's weight is analyzed as a paired observation.

This method accounts for individual variability, as it compares the difference in weights for each patient rather than treating each measurement as independent. This pairing helps to control for potential confounding variables related to patient characteristics, making it easier to attribute any observed changes directly to the diet intervention.

Other options are not suitable in this context. The independent t-test is used when comparing the means of two independent groups, which does not apply here since the same patients are measured before and after the diet. ANOVA is used when comparing means across three or more groups and is not necessary when looking at just two sets of data. Regression analysis is more appropriate for examining relationships between variables and predicting outcomes rather than simply comparing means of paired data points.