Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 15.6, Problem 6JC
To determine
Define the parameter.
State null and alternative hypothesis.
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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 15 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 15.2 - A research team wants to know if aspirin helps to...Ch. 15.2 - An allergy drug has been tested and found to give...Ch. 15.2 - The new drug is tested and the P-value is 0.0001....Ch. 15.4 - The research team that wants to know if aspirin...Ch. 15.4 - Prob. 5JCCh. 15.6 - Prob. 6JCCh. 15.6 - Prob. 7JCCh. 15.6 - Prob. 8JCCh. 15 - Better than aspirin? A very large study showed...Ch. 15 - Psychic A friend of yours claims to be psychic....
Ch. 15 - Parameters and hypotheses For each of the...Ch. 15 - Hypotheses and parameters As in Exercise 3, for...Ch. 15 - SECTION 15.2 5. Better than aspirin again?...Ch. 15 - GRE performance A test preparation company claims...Ch. 15 - SECTION 15.3 7. Hispanic origin According to the...Ch. 15 - Empty houses According to the 2010 Census, 11.4%...Ch. 15 - Prob. 9ECh. 15 - Marriage In 1960, census results indicated that...Ch. 15 - Prob. 11ECh. 15 - Golf balls The United States Golf Association...Ch. 15 - Prob. 13ECh. 15 - Prob. 14ECh. 15 - CHAPTER EXERCISES 15. Hypotheses Write the null...Ch. 15 - More hypotheses Write the null and alternative...Ch. 15 - Negatives After the political ad campaign...Ch. 15 - Dice The seller of a loaded die claims that it...Ch. 15 - Prob. 19ECh. 15 - Cars A survey investigating whether the proportion...Ch. 15 - Prob. 21ECh. 15 - Prob. 22ECh. 15 - Prob. 23ECh. 15 - Prob. 24ECh. 15 - Dowsing In a rural area, only about 30% of the...Ch. 15 - Abnormalities In the 1980s, it was generally...Ch. 15 - Prob. 27ECh. 15 - Educated mothers The National Center for Education...Ch. 15 - Contributions, please II We learned in Chapter 13,...Ch. 15 - Prob. 30ECh. 15 - Prob. 31ECh. 15 - Scratch and dent An appliance manufacturer...Ch. 15 - Prob. 33ECh. 15 - Football 2016 During the first 15 weeks of the...Ch. 15 - WebZine A magazine is considering the launch of an...Ch. 15 - Seeds A garden center wants to store leftover...Ch. 15 - Prob. 37ECh. 15 - Prob. 38ECh. 15 - Prob. 39ECh. 15 - Acid rain A study of the effects of acid rain on...Ch. 15 - Prob. 41ECh. 15 - TV ads A start-up company is about to market a new...Ch. 15 - Prob. 43ECh. 15 - Prob. 44ECh. 15 - Normal temperature again From the measurements of...Ch. 15 - Hot dogs again The nutrition lab in Chapter 14,...Ch. 15 - Prob. 47ECh. 15 - Computer lab fees again The technology committee...Ch. 15 - More Ruffles Recall from Chapter 14, Exercise 55...Ch. 15 - More Doritos We saw in Chapter 14, Exercise 56...Ch. 15 - Prob. 51ECh. 15 - Prob. 52ECh. 15 - Prob. 53ECh. 15 - Prob. 54ECh. 15 - Maze Here are the data from the researcher...Ch. 15 - Facebook friends According to...Ch. 15 - Maze revisited A student resampled the Maze times...Ch. 15 - Prob. 58ECh. 15 - Prob. 59ECh. 15 - Prob. 60E
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