Intro Stats
4th Edition
ISBN: 9780321825278
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
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Chapter 13, Problem 14E
To determine
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Identify whether the probability that a person is younger than 50 has increased by using the extra information.
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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.
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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
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d) Suggest at least two remedies to improve the model, based on the residual analysis.
Chapter 13 Solutions
Intro Stats
Ch. 13.1 - Prob. 1JCCh. 13.3 - Prob. 2JCCh. 13.4 - Prob. 3JCCh. 13 - Pet ownership Suppose that 25% of people have a...Ch. 13 - Cooking and shopping Forty-five percent of...Ch. 13 - Sports What is the probability that a person likes...Ch. 13 - Prob. 4ECh. 13 - Late to the train A student figures that he has a...Ch. 13 - Field goals A nervous kicker usually makes 70% of...Ch. 13 - Titanic On the Titanic, the probability of...
Ch. 13 - Prob. 8ECh. 13 - Facebook Facebook reports that 70% of its users...Ch. 13 - Prob. 10ECh. 13 - Prob. 11ECh. 13 - Prob. 12ECh. 13 - Prob. 13ECh. 13 - Prob. 14ECh. 13 - Prob. 15ECh. 13 - Prob. 16ECh. 13 - Prob. 17ECh. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Prob. 20ECh. 13 - Prob. 21ECh. 13 - 22. Pets In its monthly report, the local animal...Ch. 13 - Health The probabilities that an adult American...Ch. 13 - Immigration The table shows the political...Ch. 13 - Prob. 25ECh. 13 - Prob. 26ECh. 13 - Prob. 27ECh. 13 - Prob. 28ECh. 13 - Prob. 29ECh. 13 - Prob. 30ECh. 13 - Batteries A junk box in your room contains a dozen...Ch. 13 - Prob. 32ECh. 13 - Eligibility A university requires its biology...Ch. 13 - Benefits Fifty-six percent of all American workers...Ch. 13 - Prob. 35ECh. 13 - Prob. 36ECh. 13 - Prob. 37ECh. 13 - Prob. 38ECh. 13 - Unsafe food Early in 2010, Consumer Reports...Ch. 13 - 40. Birth order, finis In Exercises 20 and 26, we...Ch. 13 - Prob. 41ECh. 13 - Prob. 42ECh. 13 - Prob. 43ECh. 13 - Prob. 44ECh. 13 - Prob. 45ECh. 13 - Cars A random survey of autos parked in student...Ch. 13 - Prob. 47ECh. 13 - Prob. 48ECh. 13 - Prob. 49ECh. 13 - Prob. 50ECh. 13 - Prob. 51ECh. 13 - Prob. 52ECh. 13 - Prob. 53ECh. 13 - Prob. 54ECh. 13 - Drunks Police often set up sobriety...Ch. 13 - No-shows An airline offers discounted...Ch. 13 - Prob. 57ECh. 13 - Parts A company manufacturing electronic...Ch. 13 - HIV testing In July 2005, the journal Annals of...Ch. 13 - Polygraphs Lie detectors are controversial...
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