Hospital length of stay. Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS in the United States is $4.5$ days (Healthcare Cost and Utilization Project Statistical Brief, October 2014). A random sample of 20 hospitals in one state had a mean LOS of $3.8$ days and a standard deviation of $1.2$ days. What is meant by the phrase "90% confidence interval"?

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken, what is the probability that the mean cholesterol level of the sample:

c) Will be less than 200?

Family First Healthcare operates two medical groups, one in Philadelphia and one in Baltimore. The semiannual bonus plan for each medical group’s president has three components: a. Profitability performance. Add 0.75% of operating income. b. Average patient waiting time. Add $40,000 if the average waiting time for a patient to see a doctor after the scheduled appointment time is less than 10 minutes. If average patient waiting time is more than 10 minutes, add nothing. c. Patient satisfaction performance. Deduct$45,000 if patient satisfaction (measured using a survey asking patients about their satisfaction with their doctor and their overall satisfaction with Family First Healthcare) falls below 70 on a scale from 0 (lowest) to 100 (highest). No additional bonus is awarded for satisfaction scores of 70 or more.

$$\begin{matrix} \text{} & \text{January-June} & \text{July-December}\\ \text{Philadelphia} & \text{} & \text{}\\ \text{Operating income} & \text{\$10,250,000} & \text{\$10,600,000}\\ \text{Average waiting time} & \text{8 minutes} & \text{12 minutes}\\ \text{Patient satisfaction} & \text{77} & \text{71}\\ \text{Baltimore} & \text{} & \text{}\\ \text{Operating income} & \text{\$9,000,000} & \text{\$7,500,000}\\ \text{Average waiting time} & \text{15 minutes} & \text{8 minutes}\\ \text{Patient satisfaction} & \text{64} & \text{73}\\ \end{matrix}$$

1. Compute the bonuses paid in each half year of 2017 to the Philadelphia and Baltimore medical group presidents. 2. Discuss the validity of the components of the bonus plan as measures of profitability, waiting time performance, and patient satisfaction. Suggest one shortcoming of each measure and how it might be overcome (by redesign of the plan or by another measure). 3. Why do you think Family First Healthcare includes measures of both operating income and waiting time in its bonus plan for group presidents? Give one example of what might happen if waiting time was dropped as a performance measure.

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken,

c) What would its standard deviation be?

MGM Resorts International owns and operates hotels and casinos including the MGM Grand and the Bellagio in Las Vegas, Nevada. As of a recent year, MGM reported accounts receivable of $415,654,000 and allowance for doubtful accounts of$93,760,000. Johnson & Johnson manufactures and sells a wide range of healthcare products including Band-Aids and Tylenol. As of a recent year, Johnson & Johnson reported accounts receivable of $10,114,000,000 and allowance for doubtful accounts of$340,000,000. b. Compute the percentage of the allowance for doubtful accounts to the accounts receivable, for Johnson & Johnson. Round to one decimal place.

Healthcare professionals cite an enormous number of health problems related to obesity, and many people have an understandable desire to attain a healthy weight. There are many diet programs, services, and products on the market to aid those who wish to lose weight. If a close friend was considering purchasing or participating in one of these products, programs, or services, how would you make sure your friend was fully aware of the potential consequences of this decision? What sort of information would you want to review before making such an investment or lifestyle change yourself?

Let's say the president of the United States wishes to estimate the percentage of the population that agrees with his present stance on changes to the healthcare system. The estimate must be within.04 of the actual proportion, according to the president. Count on a 95% level of certainty. The political advisers to the president located a comparable poll from two years prior that showed 60% of respondents were in favour of making changes to the health care system. Using this, find how large of a sample is required?

In the first year after its release, 83 percent of emergency room doctors were estimated to have tried Dermabond glue (an alternative to sutures in some situations). (a) What kind of probability is this? (b) How was it probably estimated? (c) Why might the estimate be inaccurate? (Data are from Modern Healthcare 29, no. 32 [August 9, 1999], p. 70.)

MGM Resorts International owns and operates hotels and casinos including the MGM Grand and the Bellagio in Las Vegas, Nevada. As of a recent year, MGM reported accounts receivable of $415,654,000 and allowance for doubtful accounts of$93,760,000. Johnson & Johnson manufactures and sells a wide range of healthcare products including Band-Aids and Tylenol. As of a recent year, Johnson & Johnson reported accounts receivable of $10,114,000,000 and allowance for doubtful accounts of$340,000,000.

Discuss possible reasons for the difference in the two ratios computed in (a) and (b).

The latest available data showed health expenditures were $\$ 8086$ per person in the United States or $17.6 \%$ of gross domestic product. Use $\$ 8086$ as the population mean and suppose a survey research firm will take a sample of 100 people to investigate the nature of their health expenditures. Suppose the population standard deviation is $\$ 2500$.

a. Show the sampling distribution of the mean amount of healthcare expenditures for a sample of 100 people.

GfK Roper Consulting gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They requested people in many different cultures how they felt about the following statement: I try to avoid eating fast foods. In a random sample of 800 respondents, 411 people were 35 years old or younger, and, of those, 197 agreed ( completely or somewhat), with the statement. Of the 389 people over 35 years old, 246 people agreed with the statement.

b) Provide a 90% confidence interval for the difference in proportions.

Merck & Co., Inc. and Johnson & Johnson are two leading producers of healthcare products. Each has considerable assets, and each expends considerable funds each year toward the development of new products. The development of a new healthcare product is often very expensive, and risky. New products frequently must undergo considerable testing before approval for distribution to the public. For example, it took Johnson & Johnson 4 years and $200 million to develop its 1-DAY ACUVUE contact lenses. Below are some basic data compiled from the financial statements of these two companies.

$$\begin{array}{lccc} {\text{(all dollars in millions)}}&\underline{\hspace{2pt}\text{Johnson \& Johnson}\hspace{2pt}}&\underline{\hspace{15pt}\text{Merck}\hspace{15pt}}\\ \text{Total assets}&\$53,317&\$42,573\\ \text{Total revenue}&47,348&22,939\\ \text{Net income}&8,509&5,813\\ \text{Research and development expense}&5,203&4,010\\ \text{Intangible assets}&11,842&2,765\\ \end{array}$$

Instructions

a. What kinds of intangible assets might a healthcare products company have? Does the composition of these intangibles matter to investors-that is, would it be perceived differently if all of Merck's intangibles were goodwill than if all of its intangibles were patents?

b. Suppose the president of Merck has come to you for advice. He has noted that by eliminating research and development expenditures the company could have reported $4 billion more in net income. He is frustrated because much of the research never results in a product, or the products take years to develop. He says shareholders are eager for higher returns, so he is considering eliminating research and development expenditures for at least a couple of years. What would you advise?

c. The notes to Merck's financial statements note that Merck has goodwill of$1.1 billion. Where does recorded goodwill come from? Is it necessarily a good thing to have a lot of goodwill on a company's books?

Although financial data are sketchy, an estimate from a construction company indicates that adding bed capacity would cost about $\$100,000$ per bed. In addition, the rate charged for the hernia surgery varies between about $\$900$ and $\$2,000$ (U.S. dollars), with an average rate of $\$1,300$ per operation. The surgeons are paid a flat $\$600$ per operation. Due to all the uncertainties in government healthcare legislation, Shouldice would like to justify any expansion within a five-year time period.

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken,

a) What shape should the sampling distribution of the mean have?