Paired Samples T-Test Use Case
The paired samples t-test is used to test whether two responses measured on the same statistical unit are significantly different. Mathematically, it is the same as running a single sample t-test on the delta of the two samples for each row against an assumed mean of 0.0.
For more information about the paired samples t-test, see T-Test - Paired Samples.
The difference between the paired sample t-test and the Independent Samples t-test is that in the paired test, the two samples are usually from the same data set, or closely correlated.
Paired sample t-tests can be used for before-and-after studies, such as looking at a student's test scores both before and after a course. (source) For example, see the below sample data from a puppy training program that measures the skills of the puppies before they enter the program and after the program. We might want to ask if training actually improves the puppies' scores. We could do this by running a Paired Samples t-test on the Score Before Training and the Score After Training columns. Our null hypothesis is that the mean of the difference in the values between the two columns is not statistically different from zero. We would reject the null hypothesis if the Upper One Tailed p-value is less than 0.05.