Final answer:
The independent means t-test is appropriate when observations are not related to one another and are used for two independent samples. Matched pairs t-tests are used for related observations such as pre- and post-tests. The population variance and sample size affect the execution of the test rather than the choice between independent or dependent t-tests.
Step-by-step explanation:
The independent means t-test is more appropriate when the observations are not related to one another. This type of t-test is designed to compare the means from two independent samples where the sample values selected from one population are not related to the sample values selected from the other population. An example of when an independent means t-test would be used is when comparing the weight loss results from two different diet programs with two separate groups of participants.
On the other hand, a dependent or matched pairs t-test is utilized when there's a relationship between observations, such as a pre-test and post-test given to the same individuals. In this scenario, the same participants are measured twice, which makes their observations related. Lastly, not knowing the population variance and having a small sample size do not dictate which test to use; instead, they affect how the t-test is conducted, possibly requiring an estimation of the variance or using a Student's t-test if the standard deviation is unknown and the sample size is small.