Chapter 14, Problem 59E

Exercises 57 through 60 refer to the following story (see also Exercise 32): The Dean of Students at Tasmania State University wants to determine how many undergraduates at TSU are familiar with a new financial aid program offered by the university. There are 15,000 undergraduates at TSU, so it is too expensive to conduct a census. The following sampling method, known as systematic sampling, is used to choose a representative sample of undergraduates to poll. Start with the registrar’s alphabetical listing containing the names of all undergraduates. Randomly pick a number between 1 and 100, and count that far down the list. Take that name and every 100th name after it. For example, if the random number chosen is 73, then pick the 73rd, 173rd, 273rd, and so forth, names on the list.

a. Explain why the method used for choosing the sample is not simple random sampling.

b. If $100\%$ of those responding claimed that they were not familiar with the new financial aid program offered by the university, is this result more likely due to sampling variability or to sample bias? Explain.