Hospitals.
Most patients who undergo surgery make routine recoveries and are discharged as planned. Others suffer excessive bleeding, infection, or other post-surgical complications and have their discharges from the hospital delayed.
Suppose your city has a large hospital and a small hospital, each performing major and minor surgeries. You collect data to see how many surgical patients have their discharges delayed by post-surgical complications, and you find the results shown in the following table.
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Discharge Delayed
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Large Hospital
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Small Hospital
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Procedure
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Major Surgery
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120 of 800
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10 of 50
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Minor Surgery
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10 of 200
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20 of 250
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a) Overall, for what percent of patients was discharge delayed?
b) Were the percentages different for major and minor surgery?
c) Overall, what were the discharge delay rates at each hospital?
d) What were the delay rates at each hospital for each kind of surgery?
e) The small hospital advertises that it has a lower rate of postsurgical complications. Do you agree?
f) Explain, in your own words, why this confusion occurs.