A New England Journal of Medicine study November 1986 found

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.

(a) Estimate p1, p2, and p3 with 95% confidence intervals. Interpret the results.

(b) Let H0 be the null hypothesis stating p1=0.7, p2=0.2, p3=0.1. Formulate an appropriate alternative hypothesis Ha. Then test H0 using =0.01.

Solution

(a)

Using Excel the obtained output for the 95% confidenc einterval for these three proportions are,