2. (a) The overall sampling design is a two-stage stratified cluster design. The first stage consists of randomly selecting precincts (with the probability of selection proportionate to precinct size). The second stage consists of randomly selecting voters within each selected precinct. For the nation as a whole, precincts are stratified by state; and for each state, precincts are stratified by county.

(b) There are actually two sampling frames, one for each stage of sample selection. For the first stage, the sampling frame consists of the complete list of precincts within each state. For the second stage, the frame consists of a rule defining membership rather than a list; that is, the frame is all voters who vote at each selected precinct from opening until about an hour before closing.

(c) Yes; the nation as a whole is stratified by state, and the list of precincts in each state is stratified by county.

(d) Systematic sampling is used to select voters within each precinct.

(e) Random sampling error would make the mid-day margin of error larger because the sample size would be smaller: the smaller the sample, the larger the error. Sampling bias may occur because (1) those who vote early may differ systematically from those who vote later in the day; for example, the elderly, unemployed, and stay-at-home parents may be more likely to vote early in the day. Or, (2) there may be more refusals to cooperate early in the day, when people are in a hurry to get to work, than later in the day.

(f) Coverage error must be assessed with respect to each sampling frame. Assuming that the list of precincts in each county is complete, there is no coverage error in the first sampling frame; however, coverage error is introduced in the second frame insofar as no voters are chosen in the last hour before the polls close.

3. The sampling design for the 2006 GSS is a stratified multistage cluster sample with probability-proportionate-to-size selection of areas in successive stages. Table A.4 in Appendix A outlines the design. The first stage consists of tracts or counties, which are selected within stratified Standard Metropolitan Statistical Areas or counties; the second stage consists of smaller tracts or segments; and the final stage consists of housing units. Since 1972 the sampling design has changed in many ways. From 1972 to 1974, the GSS used a modified probability design with quota sampling at the final stage or block level; in 1975 and 1976, the GSS used a “transitional” design with one-half full probability and one-half block quota; since then the GSS has used a full probability sample. In addition, the sampling frames have changed over the years as the primary and secondary units have been redefined.

4. (a) The target population is all state firefighters at the time of the survey.

(b) Assuming information is available on the size of each department (i.e., the number of firefighters) and a list of firefighters can be obtained from each, you could draw a two-stage probability sample. First randomly select departments with the probability of selection proportionate to size; then randomly select a predetermined number of firefighters within each selected department. If information on the gender of each firefighter is available at the second stage of selection, you could use disproportionate stratified sampling to select subsamples of male and female firefighters; however, if this information is not available, then you would have to draw a sample large enough to provide reasonably accurate information on female firefighters—say, a sample of 500, which should have around 50 women firefighters on average.

(c) The use of a mail questionnaire survey and the existence of a complete list of the target population make it efficient to draw a simple random sample. Because information is unavailable on the gender of each firefighter, you would have to draw a sample large enough to provide reasonably accurate information on female firefighters.

5. One might respond by saying, first, that it is the absolute size of the sample rather than the proportion of the population sampled that determines precision, and second, that the sample need not be exceedingly large to yield precise results. For a sample size of 400, the margin of error for a percentage is about plus or minus 5 percent.