APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 1.5, Problem 8SE
Recently, the same five winning numbers (4, 21, 23, 34, 39) came up both on Monday and on Wednesday in the North Carolina Lottery. “That’s so unlikely that it must be rigged." said Mary. Which fallacy, if any, do you see in Mary’s reasoning?
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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.
Chapter 1 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
Ch. 1.3 - Give an example of how statistics might be useful...Ch. 1.3 - Give an example of how statistics might be useful...Ch. 1.3 - (a) Should the average business school graduate...Ch. 1.3 - Many college graduates will not use very much...Ch. 1.5 - Recently, the same five winning numbers (4, 21,...Ch. 1.5 - A National Health Interview Survey conducted by...Ch. 1.5 - A study found that radar detector users have lower...Ch. 1.5 - A lottery winner told how he picked his six-digit...Ch. 1.5 - Smokers are much more likely to speed, run red...Ch. 1.5 - An ad for a cell phone service claims that its...
Ch. 1.5 - What logical or ethical problems do you see in...Ch. 1.5 - A recent study of 231,164 New Jersey heart attack...Ch. 1.5 - When Pennsylvania repealed a law that required...Ch. 1 - Define (a) statistic; (b) statistics.Ch. 1 - List three reasons to study statistics.Ch. 1 - List three applications of statistics.Ch. 1 - List four skills needed by statisticians. Why are...Ch. 1 - List three practical challenges faced by...Ch. 1 - List three ethical challenges faced by...Ch. 1 - List five pitfalls or logical errors that may...Ch. 1 - A survey of beginning students showed that a...Ch. 1 - Under a recent U.S. Food and Drug Administration...Ch. 1 - A statistical consultant was retained by a linen...Ch. 1 - Ergonomics is the science of making sure that...Ch. 1 - Analysis of 1,064 deaths of famous popular...Ch. 1 - A recent study showed that women who lived near a...Ch. 1 - Lacrosse helmets are not needed, said Tom. None of...Ch. 1 - A European study of thousands of men found that...Ch. 1 - A research study showed that 7 percent of A...Ch. 1 - A research study showed that adolescents who...Ch. 1 - The Graduate Management Admission Test (GMAT) is...Ch. 1 - (a) Which of these two displays (table or graph)...Ch. 1 - (a) Which of these two displays (table or graph)...
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