1.2 - Populations and Random Samples

In trying to answer each of our research questions, whether yours or mine, we unfortunately can't ask every person in the population. Instead, we take a random sample from the population, and use the resulting sample to learn something, or make an inference, about the population:

POPULATION SAMPLE Sampling Inference

For the research question "what percentage of college students feel sleep-deprived?", the population of interest is all college students. Therefore, assuming we are restricting the population to be U.S. college students, a random sample might consist of 1300 randomly selected students from all of the possible colleges in the United States. For the research question, "what is the probability that a randomly selected Penn State student gets more than 7 hours of sleep each night?", the population of interest is a little narrower, namely only Penn State students. In this case, a random sample might consist of, say, 300 randomly selected Penn State students. For the research question "what is the typical number of credit cards owned by Stat 414 students?", the population of interest is even more narrow, namely only the students enrolled in Stat 414. Ahhhh! If we are only interested in students currently enrolled in Stat 414, we have no need for taking a random sample. Instead, we can conduct a census, in which all of the students are polled.

Try It! Section

Identify the population and describe a potential random sample for the research question "do women typically cry more than men?"
The population is all women and all men, at least 18 years of age, perhaps. One possible sample is 50 randomly selected women and 50 randomly selected men.

Now, for each of the research questions you previously defined, identify the population of interest and describe a potential random sample.

The answers (or data) we get to our research questions of course depend on who ends up in our random sample. We can't possibly predict the possible outcomes with certainty, but we can at least create a list of possible outcomes.