Question: A New England Journal of Medicine study found that a substantial portion of acute hospital care is 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 the admissions were judged to be appropriate, \(23 \%\) were deemed inappropriate, and the remaining \(17 \%\) could have been avoided by the use of ambulatory surgery. Let \(\mathrm{p}_{1}, \mathrm{p}_{2}\) and \(\mathrm{p}_{3}\) be the true percentages of hospital admissions in the three categories: appropriate, inappropriate and avoidable by ambulatory surgery, respectively. At a significance level of \(\alpha=0.1\), test the null hypothesis:

\(\mathrm{H}_{0}: \quad \mathrm{p}_{1}=0.8\)

\(\mathrm{H}_{\mathrm{a}}: \quad\) At least one of the multinomial probabilities does not equal its hypothesized value.

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