EXAMPLE 5.2

Simulate a random sample. Let’s simulate drawing simple random samples (SRSs) of size 100 from the population of undergraduates. Suppose that, in fact, 90% of the population owns a cell phone. Then the true value of the parameter we want to estimate is p = 0.9. (Of course, we would not sample in practice if we already knew that p = 0.9. We are sampling here to understand how the statistic behaves.)

For cell phone ownership, we can imitate the population by a table of random digits, with each entry standing for a person. Nine of the 10 digits (say, 0 to 8) stand for students who own a cell phone. The remaining digit, 9, stands for those who do not. Because all digits in a random number table are equally likely, this assignment produces a population proportion of cell phone owners equal to p = 0.9. We then simulate an SRS of 100 students from the population by taking 100 consecutive digits from Table B. The statistic is the proportion of 0s to 8s in the sample.

Here are the first 100 entries in Table B with digits 0 to 8 highlighted:

There are 90 digits between 0 and 8, so . We are fortunate here that our estimate is the true population value p = 0.9. A second SRS based on the second 100 entries in Table B gives a different result, . The third SRS gives the result . All three sample results are different. That’s sampling variability.