Mind on Statistics
5th Edition
ISBN: 9781285463186
Author: Jessica M. Utts, Robert F. Heckard
Publisher: Brooks Cole
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Textbook Question
Chapter 1, Problem 1.2E
A five-number summary for the heights in inches of the women who participated in the survey in Case Study 1.1 is as shown:
- What is the
median height for these women? - What is the
range of heights—that is, the difference in heights between the shortest woman and the tallest woman? - What is the interval of heights containing the shortest one-fourth of the women?
- What is the interval of heights containing the middle one-half of the women?
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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.
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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
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The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
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R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
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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].
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Chapter 1 Solutions
Mind on Statistics
Ch. 1 - Refer to the data and five-number summaries given...Ch. 1 - A five-number summary for the heights in inches of...Ch. 1 - In recent years, Vietnamese American women have...Ch. 1 - The risk of getting lung cancer at some point in...Ch. 1 - Refer to Case Study 1.3, in which teens were asked...Ch. 1 - Using Case Study 1.6 as an example, explain the...Ch. 1 - A CBS News poll taken in December 2009, asked a...Ch. 1 - A telephone survey of 2000 Canadians conducted...Ch. 1 - In Case Study 1.3, the margin of error for the...Ch. 1 - About how many people would need to be in a random...
Ch. 1 - Prob. 1.11ECh. 1 - Prob. 1.12ECh. 1 - Prob. 1.13ECh. 1 - For each of the studies described, explain whether...Ch. 1 - Prob. 1.15ECh. 1 - Suppose that an observational study showed that...Ch. 1 - A randomized experiment was done in which...Ch. 1 - Explain the distinction between statistical...Ch. 1 - A (hypothetical) study of what people do in their...Ch. 1 - Prob. 1.20ECh. 1 - Refer to Case Study 1.6, in which the relationship...Ch. 1 - Students in a statistics class at Penn State were...Ch. 1 - Prob. 1.23ECh. 1 - Prob. 1.24ECh. 1 - An article in the magazine Science (Service, 1994)...Ch. 1 - Prob. 1.26ECh. 1 - Prob. 1.27ECh. 1 - Prob. 1.28ECh. 1 - Refer to the study in Exercise 1.28, in which...Ch. 1 - Prob. 1.30ECh. 1 - Prob. 1.31ECh. 1 - Prob. 1.32ECh. 1 - Prob. 1.33ECh. 1 - Prob. 1.34ECh. 1 - Refer to Exercise 1.33. The Roper Organization...Ch. 1 - Prob. 1.36ECh. 1 - Prob. 1.37ECh. 1 - Prob. 1.38ECh. 1 - Prob. 1.39ECh. 1 - Prob. 1.40ECh. 1 - Prob. 1.41ECh. 1 - Suppose you were to read the following news story:...Ch. 1 - Refer to Case Study 1.5. Explain what mistakes...Ch. 1 - Refer to Case Study 1.6. Go through the five steps...
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