# Problem 1. A New England Journal of Medicine study (November 1986) found that a substantial portion of acute hospital care

Problem 1. A New England Journal of Medicine study (November 1986) found that a
substantial portion of acute hospital care is reported to be unnecessary. The physicians who conducted
the study reviewed the medical records of 1,132 patients hospitalized at six different locations across
the country. Overall, 60% of admissions in the sample were judged to be appropriate, 23% were
deemed inappropriate, whereas 17% could have been avoided by the use of ambulatory surgery. Let p1,
p2, and p3 represent the true percentages of hospital admissions in the three aforementioned categories:
appropriate, inappropriate, and avoidable by ambulatory surgery, respectively. Using the techniques
from categorical data analysis in a “one-way table”, answer the following questions:
(a) Construct 95% confidence intervals for p1, p2, and p3.
(b) Let H0 be the null hypothesis stating that p1=0.65, p2=0.20, p3=0.15. Formulate an
appropriate alternative hypothesis Ha, and then test H0 using α =0.05.