Statistics 522: Problem Set No. 1
Book Problems
For each of the following surveys, describe the target population, sampling frame, sampling unit,
and observation unit. Discuss any possible sources of selection bias or inaccuracy of responses.
•Lohr 1.7 Exercise 4 A sample of 8 architects was chosen in a city with 14 architects and
architectural firms. To select a survey sample, each architect was contacted by telephone in
order of appearance in the telephone directory. The first 8 agreeing to be interviewed formed
the sample.
•Lohr 1.7 Exercise 12 The June 1994 issue of PC World (on newsstands, May 1994) in-
cluded a report on reliability and service support for personal computers (PC’s). One of the
conclusions, “25% of new PC’s have problems,” formed the top headline of the May 23, 1994,
issue of USA Today. Every issue of PC World since October 1993 had included a survey form
asking questions about users’ hardware troubles. Survey respondents for each month were
entered in a drawing to win a new PC, and over 45,000 responses were received.
•Lohr 1.7 Exercise 16 Mutations of the BRCA 1 gene on chromosome 17 have been shown
to be associated with higher risk of breast and ovarian cancer. Ford et al (1994) studied
cancer risks in BRCA 1-mutation carriers, using a sample of 33 families in North America
and Western Europe. The families were selected by researchers who study breast cancer. Each
family in the sample had at least four persons who had been diagnosed with breast or ovarian
cancer before age 60. The researchers estimated breast and ovarian cancer risk from the
occurrence of second cancers in individuals with breast cancers and estimate a “cumulative
risk of breast cancer in gene carriers of 87% by age 70.” They concluded: “This study confirms
that BRCA1-gene carriers have a lifetime risk of either breast or ovariance cancer of close to
100%, and that carriers previously with one cancer have a high risk of developing a second
breast or ovarian cancer and need to be managed accordingly” (page 694). Based on the high
calculated risks from this analysis and samples with similar designs, many physicians have
recommended that women with a family history of breast cancer have genetic testing; some
women have undergone prophylactic mastectomies after discovering they are likely to have
the gene.
1. Answer the general questions about target population, sampling frame, and units for
this sample.
2. Does this study provide an estimate of the probability that a woman having the gene
will develop breast or ovarian cancer? Explain.
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