Final answer:
The Wilcoxon signed-rank test is the statistical test that compares the smaller sum of the signed ranks to the critical value of T to determine statistical significance for matched or paired samples.
Step-by-step explanation:
The statistical test in which the smaller sum of the signed ranks is compared to the critical value of T is the Wilcoxon signed-rank test. This is a non-parametric test that is used to compare matched or paired samples to find out if their population mean ranks differ. It is appropriate to use this test when the data can be assumed to be paired and when a parametric test, such as the Student's t-test, is not suitable, often due to the data not being normally distributed or the sample size being too small. The Wilcoxon signed-rank test involves ranking each pair's differences, assigning positive or negative signs based on the direction of the difference, and then calculating the sum of the ranks for the positive and negative differences separately. The smaller of these sums is then compared to a critical value from a reference table to determine if there is a statistically significant difference.