A clinical study investigates a possible impact of a given medication on the systolic blood pressure. In the context of that study, the systolic blood pressure of n = 20 patients was measured immediately before the medication intake as well as 1 hour after the medication intake.

The systolic blood pressure (in mmHg) before the medication intake was given by

129, 90, 130, 123, 141, 104, 168, 96, 108, 117, 139, 148, 76, 141, 117, 94, 99, 130, 91, 129,

the systolic blood pressure (in mmHg) 1 hour after the medication intake was given by

80, 100, 103, 110, 105, 85, 120, 75, 100, 101, 107, 120, 89, 110, 115, 75, 80, 95, 99, 106.

For instance, the first patient had the systolic blood pressure of 129 mmHg before taking the medication and the systolic blood pressure of 80 mmHg 1 hour after the medication intake.

1. Suggest an appropriate model to check whether the given medication has impact on the systolic blood pressure. Which assumption should we impose on the data above to apply that model?
2. We assume that the medication leads to a decrease in the systolic blood pressure. Formulate an appropriate test problem and use the corresponding p-value to decide on this assumption.