to which the person is overweight. Suppose that the distribution of the
body mass index for men has a standard deviation ofs¼3 kg/m^2 , and
we wish to estimate the meanmusing a sample of sizen¼49. Find the
probability that we would be correct within 1 kg/m^2.
4.3 Self-reported injuries among left- and right-handed people were com-
pared in a survey of 1896 college students in British Columbia, Canada.
Of the 180 left-handed students, 93 reported at least one injury, and 619
of the 1716 right-handed students reported at least one injury in the same
period. Calculate the 95% confidence interval for the proportion of stu-
dents with at least one injury for each of the two subpopulations, left-
and right-handed students.
4.4 A study was conducted to evaluate the hypothesis that tea consumption
and premenstrual syndrome are associated. A total of 188 nursing stu-
dents and 64 tea factory workers were given questionnaires. The preva-
lence of premenstrual syndrome was 39% among the nursing students
and 77% among the tea factory workers. Calculate the 95% confidence
interval for the prevalence of premenstrual syndrome for each of the two
populations, nursing students and tea factory workers.
4.5 A study was conducted to investigate drinking problems among college
students. In 1983, a group of students were asked whether they had ever
driven an automobile while drinking. In 1987, after the legal drinking
age was raised, a di¤erent group of college students were asked the same
question. The results are given in Table E4.5. Calculate, separately for
1983 and 1987, the 95% confidence interval for the proportion of stu-
dents who had driven an automobile while drinking.TABLE E4.5
Year
Drove While
Drinking 1983 1987 Total
Yes 1250 991 2241
No 1387 1666 3053
Total 2637 2657 52944.6 In August 1976, tuberculosis was diagnosed in a high school student
(INDEX CASE) in Corinth, Mississippi. Subsequently, laboratory
studies revealed that the student’s disease was caused by drug-resistant
tubercule bacilli. An epidemiologic investigation was conducted at the
high school. Table E4.6 gives the rates of positive tuberculin reaction,
determined for various groups of students according to degree of expo-
sure to the index case. Calculate the 95% confidence interval for the rate174 ESTIMATION OF PARAMETERS