Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
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Chapter 2, Problem 19P
Suppose that the average waiting time for a patient at a physician’s office is just over 29 minutes. To address the issue of long patient wait times, some physicians’ offices are using wait-tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (in minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with such systems.
- a. What are the
mean andmedian patient wait times for offices with a wait-tracking system? What are the mean and median patient wait times for offices without a wait-tracking system? - b. What are the variance and standard deviation of patient wait times for offices with a wait-tracking system? What are the variance and standard deviation of patient wait times for visits to offices without a wait tracking system?
- c. Create a box plot for patient wait times for offices without a wait-tracking system.
- d. Create a box plot for patient wait times for offices with a wait-tracking system.
- e. Do offices with a wait-tracking system have shorter patient wait times than offices without a wait-tracking system? Explain.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 2 Solutions
Essentials Of Business Analytics
Ch. 2 - A Wall Street Journal subscriber survey asked 46...Ch. 2 - The following table contains a partial list of...Ch. 2 - Ohio Logistics manages the logistical activities...Ch. 2 - A partial relative frequency distribution is...Ch. 2 - In a recent report, the top five syndicated...Ch. 2 - In a study of how chief executive officers (CEOs)...Ch. 2 - Consumer complaints are frequently reported to the...Ch. 2 - Reports have found that many U.S. adults would...Ch. 2 - Consider the following data: a. Develop a...Ch. 2 - Consider the following frequency distribution....
Ch. 2 - The owner of an automobile repair shop studied the...Ch. 2 - Approximately 1.65 million high school students...Ch. 2 - Consider a sample with data values of 10, 20, 12,...Ch. 2 - Consider a sample with data values of 27, 25, 20,...Ch. 2 - Consider a sample with data values of 53, 55, 70,...Ch. 2 - If an asset declines in value from 5,000 to 3,500...Ch. 2 - Suppose that you initially invested 10,000 in the...Ch. 2 - The average time that Americans commute to work is...Ch. 2 - Suppose that the average waiting time for a...Ch. 2 - According to the National Education Association...Ch. 2 - Return to the waiting times given for the...Ch. 2 - The results of a national survey showed that on...Ch. 2 - Suppose that the national average for the math...Ch. 2 - Five observations taken for two variables follow....Ch. 2 - The scatter chart in the following figure was...Ch. 2 - The economic downturn in 20082009 resulted in the...Ch. 2 - Heavenly Chocolates manufactures and sells quality...
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