Final answer:
The paired t-test is applied to numerical data with two paired groups. It compares the means of the differences within each pair, such as the before-and-after measurements in a study. This method is commonly used in studies with small sample sizes and in cases where the samples are dependent. The correct option is C.
Step-by-step explanation:
The paired t-test is applied to numerical data with two paired groups (option C). This means that the paired t-test is a hypothesis test that compares two related samples by looking at the difference within each pair. For example, this method could be used to compare the pre-test and post-test scores of students in a classroom to determine if a new teaching method has had a statistically significant effect.
When a hypothesis test for matched or paired samples is performed, characteristics such as simple random sampling, often small sample sizes, and dependence between the two samples are important. Explanation of this requires knowing that in matched samples, the two measurements typically come from the same pair of individuals or objects, for instance, and the means of the differences are compared rather than the individual means themselves.
A practical example of a matched or paired samples situation is when a group of students measures their anxiety levels at the start and end of a quarter to see if a new technique has lowered their anxiety levels. Given the paired nature of the data (e.g., (1,000, 900); (1,200, 1,050)), this is a case for a paired t-test.