- Sample Space
- The
**sample space**(or**outcome space**), denoted \(\mathbf{S}\), is the collection of all possible outcomes of a random study.

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

\(\mathbf{S} = \{\text{yes}, \text{no}\}\)

In order to answer my second research question, 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 had last night. In this case, if we let *h* denote the number of hours slept, we would write the sample space as:

\(\mathbf{S} = \{h: h \ge 0 \text{ hours}\}\)

Hmmm, if we conducted a random study to answer my 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?", we would write the sample space as:

\(\mathbf{S} = \{0, 1, 2, ..., 31\}\)

Finally, if we were interested in learning about students who took Stat 414 in the past decade when trying to answer my fourth research question, we might ask all current Stat 414 students "how many credit cards do you have?" In that case, we would write our sample space as:

\(\mathbf{S} = \{0, 1, 2, ...\}\)

There is not always just one way of obtaining an answer to a research question. For my second research question, how would we define the sample space if we instead asked a random sample of college students "did you get more than seven hours of sleep last night?"

For each of the research questions you created:

- Formulate the question you would ask (or describe the measurement technique you would use).
- Define the resulting sample space.

Once we collect sample data, we need to do something with it. Like summarizing it would be good! How we summarize data depends on the type of data we collect.