A research hospital is testing a blood pressure medicine, hoping to observe a drop of 10mmHg after a week of treatment. They also wants to compare the lowering from this medicine with that from the standard medicine. They recruit two groups of patients to compare the new medicine (Group A) and standard medicine (Group B). They were not able to recruit groups which were suitable for matched pairs design.

Consider the standard error needed for the hypothesis test that the Group A patients had a drop of 10mmHg and the standard error needed for the hypothesis test comparing the drops of Group A and Group B. How would these standard errors compare? [ Select ] ["The standard error for the Group A test would always be smaller than that of the comparison test.", "These two standard errors would always be the same.", "It depends on the sample sizes.", "The standard error for the Group A test would always be larger than that for the comparison test.", "It depends on the data (observed drops and their difference)."]

Consider the P-value for the hypothesis test that the Group A patients had a drop of 10mmHg and the P-value for the hypothesis test comparing the drops of Group A and Group B. How would these P-values compare? [ Select ] ["These P-values would always be equal.", "It depends on the observed drops for the two groups and sample sizes.", "The P-value for the Group A test would always be bigger than that for the comparison test.", "It depends on the significance level.", "The P-value for the Group A test would always be smaller than that for the comparison test."]