A drug company is trying to compare the effectiveness of melaton in supplements and a mild sedative to see if patients with sleep problems response better under the supplement or the drug.

100 patients with similar sleep problems were selected for the study.

Statistician A suggested the following experiment:

50 patients will be randomly selected from the group and will be given the melatonin supplement every night for a month while the other 50 patients will receive the mild sedative every night for the month. Sleep records will be kept for all patients and average sleep hours per night from the monthly record for each patient will be used for the analysis. Suppose  denotes the mean sleep hour for patients taking melatonin supplement and  denotes the mean sleep hour for patients taking the sedative.

Statistician B suggested the following experiment:

All 100 patients will be given nightly melatonin supplement for one month and their average sleep hours per night will be recorded from the month-long data. After a brief break period, all 100 patients will be given the mild sedative every night for a month and average sleep hours per night for each patient will be recorded from this period as well. Suppose  denotes the mean sleep hour for patients from the period taking melatonin supplement and  denotes the mean sleep hour for patients from the month taking the sedative.

The appropriate hypotheses to test for the study suggested by Statistician B is: