Final answer:
The correct answer is option B. False. The t-test does not count cases but determines if two groups' means are significantly different.
Step-by-step explanation:
The t-test is not designed to examine which of two groups has the most cases. Instead, its purpose is to determine whether there is a statistically significant difference between the means of two groups. Several types of t-tests exist, including: a test of two independent means, a test for matched pairs, and a test of a single mean. The hypothesis test on matched or paired samples involves taking two measurements from the same pair of individuals or objects, indicating that both statement B and C from the options are true, as they describe common features of matched-pair t-tests. It includes types like tests of two independent means, tests for matched pairs, and tests for a single mean. Larger sample sizes are preferred for scientific rigor.
Furthermore, in hypothesis testing for matched samples, differences are calculated for the pairs, and these differences become the data. It's also crucial to know that larger sample sizes are typically preferred over smaller ones in scientific experiments, including for tests like the Student's t-test, which accounts for small sample sizes by using a distribution that allows for more variability than the standard normal distribution.