Stats: Data and Models
5th Edition
ISBN: 9780135164013
Author: DeVeaux
Publisher: PEARSON CO
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Chapter 2, Problem 85E
To determine
Create an appropriate graph and describe the distribution.
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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
Stats: Data and Models
Ch. 2.3 - You may be surprised to find that you already have...Ch. 2.3 - Prob. 2JCCh. 2.3 - Prob. 3JCCh. 2.3 - Prob. 4JCCh. 2.3 - Prob. 5JCCh. 2.5 - Prob. 6JCCh. 2.5 - Prob. 7JCCh. 2.5 - Prob. 8JCCh. 2 - Prob. 1ECh. 2 - 2. Nonoccupant fatalities The frequencies of...
Ch. 2 - 3. Movie genres The pie chart summarizes the...Ch. 2 - 4. Movie ratings The Motion Picture Association of...Ch. 2 - Prob. 5ECh. 2 - 6. Marriage in decline Changing attitudes about...Ch. 2 - 7. Traffic fatalities 2013 Here are two histograms...Ch. 2 - 8. Traffic fatalities 2013 again Here are the same...Ch. 2 - Prob. 9ECh. 2 - Prob. 10ECh. 2 - 11. E-mails A university teacher saved every...Ch. 2 - 12. Adoptions The U.S. Census Bureau keeps track...Ch. 2 - Prob. 13ECh. 2 - Prob. 14ECh. 2 - Prob. 15ECh. 2 - Prob. 16ECh. 2 - Prob. 17ECh. 2 - Prob. 18ECh. 2 - Prob. 19ECh. 2 - Prob. 20ECh. 2 - Prob. 21ECh. 2 - 22. Adoptions III For the number of adoptions in...Ch. 2 - Prob. 23ECh. 2 - Prob. 24ECh. 2 - 33. Thinking about shape Would you expect...Ch. 2 - 34. More shapes Would you expect distributions of...Ch. 2 - Prob. 35ECh. 2 - Prob. 36ECh. 2 - Prob. 37ECh. 2 - Prob. 38ECh. 2 - Prob. 39ECh. 2 - Prob. 40ECh. 2 - Prob. 41ECh. 2 - Prob. 42ECh. 2 - Prob. 43ECh. 2 - Prob. 44ECh. 2 - 45. Cereals The histogram shows the carbohydrate...Ch. 2 - Prob. 46ECh. 2 - 47. Heart attack stays The histogram shows the...Ch. 2 - 48. *Bird species 2013 The Cornell Lab of...Ch. 2 - 49. Super Bowl points 2016 How many points do...Ch. 2 - 50. Super Bowl edge 2016 In the Super Bowl, by how...Ch. 2 - Prob. 51ECh. 2 - Prob. 52ECh. 2 - Prob. 53ECh. 2 - 54. Sick days During contract negotiations, a...Ch. 2 - 55. Floods 2015 Here are the annual numbers of...Ch. 2 - 56. Tornadoes 2015 Here are the annual numbers of...Ch. 2 - Prob. 57ECh. 2 - Prob. 58ECh. 2 - Prob. 59ECh. 2 - 60. Neck size The histogram shows the neck sizes...Ch. 2 - Prob. 61ECh. 2 - 62. Neck sizes again Look again at the histogram...Ch. 2 - 63. Movie lengths 2010 The histogram shows the...Ch. 2 - 64. Golf drives 2015 The display shows the average...Ch. 2 - Prob. 65ECh. 2 - Prob. 66ECh. 2 - Prob. 67ECh. 2 - Prob. 68ECh. 2 - Prob. 69ECh. 2 - Prob. 70ECh. 2 - Prob. 71ECh. 2 - Prob. 72ECh. 2 - Prob. 73ECh. 2 - 74. Major hurricanes 2013 The following data give...Ch. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Prob. 78ECh. 2 - Prob. 79ECh. 2 - Prob. 80ECh. 2 - Prob. 81ECh. 2 - Prob. 82ECh. 2 - Prob. 83ECh. 2 - 84. Boomtowns 2015 In 2015, the website...Ch. 2 - Prob. 85ECh. 2 - Prob. 86E
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