In order to answer the first research question above, we would need to take a random sample of college students, and ask each one "Do you consider yourself to be sleep-deprived?" Each student would reply either "yes" or "no." Therefore, we would write the sample space as:

S = {yes, no}

In order to answer the second research question above, we would need to know how many hours of sleep a random sample of college students gets each night. One way of getting this information is to ask each selected student to record the number of hours of sleep they got last night. In this case, if we let h denote the number of hours slept, we would write the sample space as:

S = {h: h ≥ 0 hours}

Hmmm, if we conducted a random study to answer the third research question, how would we define our sample space? Well, of course, it depends on how we went about trying to answer the question. If we asked a random sample of men and women "on how many days did you cry last month (August)?", we would write the sample space as:

S = {0, 1, 2, ..., 31}

Finally, in trying to answer the fourth research question, we might ask a random sample of Stat 414 students "how many credit cards do you have?" In that case, we would write our sample space as:

S = {0, 1, 2, ...}