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PROBLEMS: CHAPTER 2 1. The largest health care organization in North Texas has decided to donate money to area universities to foster and encourage these universities to incorporate more health care topics into their curriculum. It was suggested that the allocation of this money should be based on universities attended by their employees. A survey of 300 professional employees resulted in 200 who attended local universities. The universities not considered local were ignored. This data can be found in “Excel Data”, Tab C2 – Prob 1. Summarize this data for a brief presentation to management, using whatever statistical tools are appropriate. 2. The administrator of a local hospital is constantly having patients complain about the poor quality of their health care during their stay in the hospital. In order to gain more information concerning their patients perception of their quality of care, the administrator randomly select 160 recent patients and has her staff call each one on the phone and solicit their opinion as to the quality of care they received. Two patients refused to answer resulting in 158 responses. This data can be found in “Excel Data”, Tab C2 – Prob 2. Summarize this data for the administrator using whatever statistical tools are appropriate. 3. A common complaint of patients is the time they have to wait “beyond their appointment time” before they see their doctor. In order to study the extent of this problem, the doctor asked his staff to randomly pull 300 patient files and calculate the time between their appointment time and when they actually got to see the doctor [fortunately these two times were captured for each patient]. This data can be found in “Excel Data”, Tab C2 – Prob 3. Summarize this data for the administrator using whatever statistical tools are appropriate. What would you suggest to the doctor after reviewing your results. 4. Blue Cross suspects that some hospitals intentionally keep patients extra days to pad the bill. The Blue Cross statistician selected a very common and stable operation, performed very frequently by all hospitals, and pulls the number of days a patient stayed in the hospital. This data can be found in “Excel Data”, Tab C2 – Prob 4. Summarize this data for the administrator using whatever statistical tools are appropriate. Be sure to include a cross-tab. 5. In order to plan effectively, it is important that the anesthesiologist be able to estimate how long it will take for the drug to put the patient to sleep. It is known that this length of time increases with the age of the patient. In order to study this problem, a local surgical hospital agreed to collect this data for one week. This data can be found in “Excel Data”, Tab C2 – Prob 5. Summarize this data for the administrator using whatever statistical tools are appropriate. Be sure to include a scatter plot. Chapter 4 (and 3) 1. For the following data, identify whether or not they are 1. categorical [nominal or ordinal], or 2. interval/numerical [discrete or continuous] Give examples of possible values for each random variable. [Example: number of children living in a given home – “interval data [discrete], (0, 1, 2, 3, …)” a. marital status b. number of students who drop this statistics course. c. time student spends studying for their first statistics test. d. the weight loss over the first week of a “fad” diet e. the amount owed on a credit card (explain you answer) f. the part on a new automobile that breaks during the first year of ownership 2. A random sample of grade point averages for 20 students resulted in the following data. [data is sorted for you from smallest to largest] [1.84, 1.94, 2.15, 2.22, 2.37, 2.76, 2.82, 2.89, 2.94, 2.96. 2.99, 3.05, 3.11, 3.24, 3.26, 3,29, 3.33, 3.54, 3.58, 3.79] a. use 5 class intervals (cells) to describe this data in a frequency distribution, and relative frequency distribution. Relative Class Interval Frequency Frequency b. on the following graph, draw a frequency histogram. (show all relevant information on graph including relative frequency) Relative Frequency Frequency 3. Data from the last statistics course was collected on the number of hours each student studied and their grade on the final resulting in Number Hours Studied 30 22 40 Grade on Final 85 70 65 Plot a scatter diagram for this data showing the relationship between the two variables. Show all relevant information on the graph (this means it should look just like one you would put in a report prepared for President Bush). 4. The number of sick days due to colds and flu last year at UTA was recorded for 5 faculty resulting in [ 5, 4, 0, 6, 0 ]. Calculate the following statistics a. mean b. median c. variance d. standard deviation 5. The mean grade point average (gpa) for UTA students is 2.5 with a standard deviation of 0.5 a. If the histogram for gpa’s is approximately mounded, what percent of the gpa’s would you expect between 1.5 and 3.5? b. If the histogram for gpa’s is approximately mounded, what percent of the gpa’s would you expect greater than 3.5? c. If the histogram for gpa’s is NOT mounded, what percent of the gpa’s would you expect between 1.5 and 3.5? CHAPTER 6 1. Bayes's Problem: Six percent of black americans are carriers of sickle cell anemia. a new test to detect the carrier gives a positive indication 98% of the time when the individual is a carrier and gives a negative indication 94% of the time when the individual is not a carrier. A black american is selected at random from this population, given the test and reacts positively. What is the probability that he is a carrier. 2. Bayes's Problem: From past records it was determined that 20% of all hospital bills contain an error or errors. It was decided to hire a university intern to 100% inspect all records to identify incorrect ones. These then would be corrected by hospital personnel. While training the intern, it was determined that he misclassifies bills containing errors 10% of the time [if a bill contains an error, there is a 10% chance that he will not detect this error]. Also he misclassifies bills containing no error 5% of the time [if a bill contains no error, there is a 5% chance that he will classify it as containing an error]. If the hospital data base for last year contains 100,000 bills [80,000 with no errors and 20,000 with errors], (a) how many of these bills would the intern classify as containing an error, (b) of these, how many actually did not have an error. CHAPTER 7 1. Binomial Distribution: For a particular couple, both carrying a gene for Osteogenesis Imperfecta, the probability that they will have a child with this disorder is 1/4. This couple wants to have 3 children. (a) What is the probability that none of their children will have this disorder? (b)What is the probability that they will have at least one child with this disorder? 2. Poisson Distribution: Weekly inspections of the operating room for infectious bugs resulting in the quality inspector finding an average of 3.2 bugs each week. Microbiologist have determined that the distribution of the number of bugs found each week follows a poisson distribution [in this case with a mean of 3.2]. (a) what is the probability that you find 2 bugs next week? (2) what is the probability that you find more than 5 bugs next week? (3) what is the probability that you find more than 12 bugs next week? (4) if you did find 13 bugs next week, what would you conclude and tell your boss. CHAPTER 8 1. Normal Distribution: Patients tend to lose weight during hospital stays. Over the years it was determined that the weight loss for a 5 day hospital stay was approximately normal with a mean of 5 pounds and standard deviation 5 pounds. (a) What is the probability that a randomly selected patient will not lose any weight? (b) What is the probability that a patient will lose over 3.5 pounds? (c) What is the probability that a patient will lose exactly 4 pounds? (d) What is the probability that a patient will lose over 10 pounds? (e) If a patient did lose 10 pounds, what would you recommend? CHAPTER 9 1. Distribution of Sum of Random Variables: The number of minutes a nurse spends, during a 8 hour shift, with each patient in their ward is normally distributed with a mean of 20 minutes and standard deviation 5 minutes [assume the time nurses spend with patients is a function of the needs of the patient]. If the hospital budgets for each nurse to serve 22 patients [22 patients are assigned to each nurse], what is the mean and standard deviation of the total time the nurse spends on treating her 22 patients? What is the probability that the nurse has to work beyond her 8 hour shift during a randomly selected day? CHAPTER 10 CHAPTER 11 CHAPTER 12 CHAPTER 13 1. Difference in Means: A HMO has established a rule that allows billing for the average direct nursing cost per patient in the respiratory and cardiac intensive care units of hospitals [define direct nursing cost as the actual costs based on the time a nurse attends a given patient]. Unfortunately this data does not exist in any hospital data base, so the hospital hires an industrial engineer to calculate this cost for the next 100 patients in each of the two units. If the hospital can show that there is no significant difference in the average direct nursing cost between units, they will be allowed to use one estimate for each unit. Otherwise, they will be required to use a different estimate for each unit. (a) determine if there is a significant difference in the average direct nursing cost between the two units, (b) estimate the average direct nursing cost with a point estimate and 95% confidence interval [if you find a significant difference in part a, you will need an estimate for each of the two units, otherwise use all the data to estimate the average direct nursing cost] 2. Paired Difference in Means: A HMO launches an intensive campaign to increase the productivity of the health care professionals in the system with an intensive training program. Following this one month training session, the productivity of 40 randomly selected health care professionals was measured. Their productivity, before training, for these same 40 professionals was also determined. (a) did the training significantly increase their average productivity, (b) if so, by how much. By the way, this intensive training program will end up costing around $1000 per professional and there are 50,000 professionals in the HMO so it is important to make sure there actually is an increase in productivity and the magnitude of this increase is large enough to recover the cost of the training. CHAPTER 14 CHAPTER 15

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