Final answer:
The paired t-test is applicable when the observations in the two samples are paired, meaning each subject is measured twice under different conditions. This forms pairs of related observations which are then analyzed using the Student's t-distribution to compare the means of these differences.
Step-by-step explanation:
The paired t-test is applicable when the observations in the two samples are paired. This means that for a paired t-test, each subject or entity is measured twice, producing pairs of observations. These measurements are commonly based on a before-and-after scenario, such as measuring student performance on a test before and after a specific intervention, or any scenario where you would expect the measurements to be related or paired.
When performing a hypothesis test on matched or paired samples, it's important to note that the two measurements are drawn from the same pair of individuals or objects and that the sample means of these differences are compared to each other. These characteristics distinguish paired samples from independent samples, wherein the two groups would be unrelated.
Examples of matched or paired samples analysis would include instances where simple random sampling is used and where sample sizes are often small, allowing the use of Student's t-distribution to analyze the mean of the differences between paired observations.