Business Analytics, Loose-leaf Edition (3rd Edition)
3rd Edition
ISBN: 9780135231692
Author: James R. Evans
Publisher: PEARSON
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Textbook Question
Chapter 2, Problem 9PE
In the Excel file Automobile Quality, search for and add a new column for the country of origin for each brand. Then sort the data from the lowest to highest by number of problems per
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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
Business Analytics, Loose-leaf Edition (3rd Edition)
Ch. 2 - The Excel file Syringe Samples provides data for...Ch. 2 - Convert the Store and Regional Sales database to...Ch. 2 - Convert the Purchase Orders database to an Excel...Ch. 2 - Prob. 6PECh. 2 - Prob. 8PECh. 2 - In the Excel file Automobile Quality, search for...Ch. 2 - Prob. 10PECh. 2 - Conduct a Pareto analysis for the number of...Ch. 2 - Use Excels filtering capability in the Purchase...Ch. 2 - In the Sales Transactions database, use Excels...
Ch. 2 - Filter the data in the Bicycle Inventory database...Ch. 2 - Use the Excel file Credit Risk Data that was...Ch. 2 - Apply the Advanced Filter to the Credit Risk Data...Ch. 2 - Prob. 17PECh. 2 - For the Bicycle Inventory database, use database...Ch. 2 - For the Bicycle Inventory database, write a...Ch. 2 - The Excel file SP500 provides open, high, low, and...Ch. 2 - In the Purchase Orders database, we need to find...Ch. 2 - An auditor found an expense receipt for 179.24...Ch. 2 - Use PivotTables to find the number of sales...
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