Question: The student newspaper at a university in California reported a debate between two student council members, revolving around a survey of students (California Aggie, 8 November 1994, p. 3). The newspaper reported that "according to an AS [Associated Students] Survey Unit poll, 52 percent of the students surveyed said they opposed a diversity requirement." The report said that one council member "claimed that the roughly 500 people polled were not enough to guarantee a statistically sound cross section of the student population." Another council member countered by saying that "three percent is an excellent random sampling, so there's no reason to question accuracy." (Note that the 3% figure is based on the fact that there were about 17,000 undergraduate students currently enrolled at that time.)
a. Comment on the remark attributed to the first council member, that the sample size is not large enough to "guarantee a statistically sound cross section of the population." Is the size of the sample the relevant issue to address his concern?
b. Comment on the remark by the second council member that "three percent is an excellent random sampling, so there's no reason to question accuracy." Is she correct in her use of terminology and in her conclusion?
c. Assuming a random sample was used, produce an interval that almost certainly covers the true percentage of the population of students who oppose the diversity requirement. Use your result to comment on the debate. In particular, do these results allow a conclusion as to whether the majority of students on campus oppose the requirement?