2.8 Distribution of a Sample Proportion
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We presumed earlier that the sample of voters is a simple random one, and we further presumed that the people sampled will actually vote and
that they have been candid with the interviewer concerning their voting preference. Samplers commonly call these presumptions into question and
have a variety of ways of dealing with them. In addition, such samples are rarely simple random ones; all we can say here is that these variations in
the sampling design have some effect on the sampling error.
b
Exercises 2.8
1. A survey of 300 paperback novels showed that 47 could be classified as romance
novels. Find an approximate 95 confidence interval for p; the true proportion of romance paperback novels.
2. Records indicate that
1 8
of American children receive welfare payments. If this survey was based on 250 records, find an approximate 95 confidence interval for
the true proportion of children who receive welfare payments.
3. A random sample of 300 voters showed that 48 favored a candidate. Does an
approximate 95 confidence interval indicate that it is possible for the candidate to win the election?
4. A survey of 423 workers found that
1 9
were union members. Find an approximate 95 confidence interval for the true proportion of union workers.
5. The sampling error of a survey in a magazine was stated to be 5. What was the
sample size for the survey?
6. A student conducted a project for a statistics course and found that
2 3
of the respondents in interviews of 120 people did not know that the Bill of Rights is
the first ten amendments to the Constitution. Find an approximate 90 confidence interval for the true proportion of people who do not know that the Bill of Rights
is the first ten amendments to the Constitution.
7. A magazine devoted to health issues discovered that
3 5
of the time a visit to a physician resulted in a prescription. The survey was based on 130 telephone
interviews. Use this data to construct an approximate 90 confidence interval for the true proportion of patients given a prescription as a result of a visit to their
physician.
8. According to a recent study, 81 of college students say that they favor drug
testing in the workplace. The study was conducted among 400 college students. Find an approximate 90 confidence interval for the true proportion of college
students who favor drug testing in the workplace.
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Chapter 2 Discrete Random Variables and Probability Distributions
Kategori