a A unit is a freshman at a two- or four-year college or university in the United States in the Fall of 1997; the poulation is all such students; the sample is the set of 252,082 students who were surveyed.
b A stratified random sample, in which schools were the strata.
c A cluster sample, where each school is a cluster.
d It would be difficult to obtain a list of all first year students from which to select a simple random sample. It would be easier to obtain a list of schools, and then either contact each school and ask them to provide a random sample (as in b) or first slect a random sample of schools and then obtain a list of all first year students at those schools (as in c)
Problem 6.
These results are more likely to reflect what is capturing students' attention each year, rather than increased apathy. For instance, in years in which the economy is bad and jobs are scarce, students tend to be more concerned with finding jobs. In years in which there are political issues affecting students, they are more likely to be more concerned with politics.
Problem 11.
The interviewers were told only to choose respondents on specific characteristics, but not to worry about whether or not they were otherwise representative. The interviewers would undoubtly choose friends and acquaintances, which would be unlikely to produce a representative sample with regard to voting behaviour.
Problem 14.
a The sampling frame was the list of 66,000 subscribers to the dental magazines. Because Bristol Myyers was trying to extend results to all dentists this sampling frame was probably not sufficient. We would need to know whether or not all dentists were likely to subscribe to one of the magazines.
b Nonresponse was a major problem, since 10,000 dentists received the survey but fewer than 2,000 responded.
c They could have made additional attempts to get the remaining dentists in their sample to respond.
Problem 15.
a Aproximate margin of error is 1 over the square root of 756 = 0.036, or about 4%.
b The margin of error tells us that the proportion of the populations with this opinion is almost certainly within 4% of the sample proportion of 56%, or between 52% and 60%. Therefore, we should be convinced that it is mopre than 50%.
Problem 16.
a If the sample were chosen randomly, the size of the sample is the relevant issue and the size of the population does not matter. A sapmle of 500 students would have a margin of error of about 4.5%, so it may or may not be considerd large enough depending n how precise a conclusion was needed.
b The concern should not be with the percent of the populaiton that had been sampled; it should be with the actual number of students sampled. Further her use of terminology is not correct. She really means that a random sample of 500 students should be enough to provide a reasonable estimate.
c The margin of error is about 4.5% and the sample proportion is 52%, so we can be fairly certain that between 47.5% and 56.4% of all students oppose the diversity requirement. Because the interval covers 50%, we cannot make a conclusion about majority opinion.
Problem 19.
If there is little natural variability in a set of measurments then the average in the sample will more accurately reflect the average for the whole population than if there is extreme natural variability.