Final answer:
The appropriate test statistic for the relationship between pregnancy weight gain and infant's birth weight is Pearson's r, which measures the linear correlation between these two variables.
Step-by-step explanation:
When assessing the relationship between weight gain during pregnancy (the independent variable) and the infant's birth weight (the dependent variable), the appropriate test statistic to use would be Pearson's r, which is a measure of the linear correlation between two variables. The Pearson's r can tell us how strongly the two variables are related and whether the relationship is positive or negative. To verify any potential relationship, steps like drawing a scatter plot and calculating the least-squares regression line can be useful. In addition, finding the correlation coefficient and testing its significance are important to conclude if the relationship is statistically valid.