Stats
5th Edition
ISBN: 9780135163825
Author: De Veaux, Richard D., Velleman, Paul F., BOCK, David E.
Publisher: Pearson,
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Chapter R, Problem 5.29RE
To determine
Check whether the percentage of U.S businesses in Denver area owned by women, is not 36% and also state the conclusion.
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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 R Solutions
Stats
Ch. R - Prob. 1.1RECh. R - R1.2. Prenatal care Results of a 1996 American...Ch. R - R1.3. Singers by parts The boxplots display the...Ch. R - Prob. 1.4RECh. R - Prob. 1.5RECh. R - Prob. 1.6RECh. R - R1.7. State University Public relations staff...Ch. R - R1.8. Shenandoah rain Based on long-term...Ch. R - Prob. 1.9RECh. R - Prob. 1.10RE
Ch. R - Prob. 1.11RECh. R - R1.12. e-Books A study by the Pew Internet &...Ch. R - Prob. 1.13RECh. R - R1.14. Accidents Progressive Insurance asked...Ch. R - Prob. 1.15RECh. R - R1.16. Hard water II The data set from England and...Ch. R - Prob. 1.17RECh. R - R1.18. Old Faithful It is a common belief that...Ch. R - R1.19. Old Faithful? Does the duration of an...Ch. R - R1.20. Teen drivers 2013 The National Highway...Ch. R - Prob. 1.21RECh. R - Women’s Short Track 2018 The times of skaters in...Ch. R - Prob. 1.23RECh. R - R1.24. Sluggers Babe Ruth was the first great...Ch. R - Prob. 1.25RECh. R - R1.26. Music and memory Is it a good idea to...Ch. R - Prob. 1.27RECh. R - R1.28. Birth order Is your birth order related to...Ch. R - Prob. 1.29RECh. R - R1.30. Birth order revisited Consider again the...Ch. R - Prob. 1.31RECh. R - R1.32. Engines, again Horsepower is another...Ch. R - R1.33. Age and party 2011 The Pew Research Center...Ch. R - R1.34. Pay According to the Bureau of Labor...Ch. R - Prob. 1.35RECh. R - R1.36. Bike safety 2015 The Bicycle Helmet Safety...Ch. R - Prob. 1.37RECh. R - Prob. 1.38RECh. R - Prob. 1.41RECh. R - Prob. 1.42RECh. R - R1.43. Student survey investigation The Student...Ch. R - Prob. 1.44RECh. R - Prob. 2.1RECh. R - Prob. 2.2RECh. R - Prob. 2.3RECh. R - Prob. 2.4RECh. R - Prob. 2.5RECh. R - Prob. 2.6RECh. R - Prob. 2.7RECh. R - Prob. 2.8RECh. R - Prob. 2.9RECh. R - Prob. 2.10RECh. R - Prob. 2.11RECh. R - Prob. 2.12RECh. R - Prob. 2.13RECh. R - Prob. 2.14RECh. R - R2.15. Cars, correlations What factor most...Ch. R - R2.16. Cars, associations Look again at the...Ch. R - Prob. 2.17RECh. R - Prob. 2.18RECh. R - Prob. 2.19RECh. R - Prob. 2.20RECh. R - Prob. 2.21RECh. R - Prob. 2.22RECh. R - Prob. 2.23RECh. R - Prob. 2.24RECh. R - Prob. 2.25RECh. R - Prob. 2.26RECh. R - Prob. 2.27RECh. R - Prob. 2.28RECh. R - Prob. 2.29RECh. R - Prob. 2.30RECh. R - Prob. 2.31RECh. R - Prob. 2.32RECh. R - Prob. 2.33RECh. R - Prob. 2.34RECh. R - Prob. 2.35RECh. R - Prob. 2.36RECh. R - Prob. 2.37RECh. R - Prob. 2.38RECh. R - Prob. 2.39RECh. R - Prob. 2.40RECh. R - Prob. 2.41RECh. R - Prob. 2.42RECh. R - Prob. 2.43RECh. R - Prob. 2.44RECh. R - Prob. 2.45RECh. R - Prob. 2.46RECh. R - Prob. 2.47RECh. R - Prob. 2.48RECh. R - Prob. 2.49RECh. R - Prob. 2.50RECh. R - Prob. 2.51RECh. R - Prob. 2.52RECh. R - Prob. 3.1RECh. R - Prob. 3.2RECh. R - Prob. 3.3RECh. R - Prob. 3.4RECh. R - Prob. 3.5RECh. R - Prob. 3.6RECh. R - Prob. 3.7RECh. R - Prob. 3.8RECh. R - Prob. 3.9RECh. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - Prob. 3.11RECh. R - Prob. 3.12RECh. R - Prob. 3.13RECh. R - Prob. 3.14RECh. R - Prob. 3.15RECh. R - Prob. 3.16RECh. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - R3.1–R3.18. What design? Analyze the design of...Ch. R - Prob. 3.19RECh. R - Prob. 3.20RECh. R - R3.21. Alternate day fasting A paper published in...Ch. R - Prob. 3.22RECh. R - Prob. 3.23RECh. R - R3.24. Tips, take 2 In another experiment to see...Ch. R - Prob. 3.25RECh. R - Prob. 3.26RECh. R - Prob. 3.27RECh. R - R3.29. Homecoming A college statistics class...Ch. R - Prob. 3.29RECh. R - R3.31. Smoking and Alzheimer’s Medical studies...Ch. R - R3.32. Antacids A researcher wants to compare the...Ch. R - Prob. 3.32RECh. R - Prob. 3.33RECh. R - Prob. 3.34RECh. R - Prob. 3.35RECh. R - Prob. 3.36RECh. R - Prob. 3.37RECh. R - Prob. 3.38RECh. R - R3.39. Acupuncture Research reported in 2008...Ch. R - R3.40. Fuel efficiency Wayne Collier designed an...Ch. R - Prob. 3.41RECh. R - R3.42. Internet speed Carsten, Matt, and Rainer...Ch. R - Prob. 4.1RECh. R - Prob. 4.2RECh. R - Prob. 4.3RECh. R - Bipolar Psychiatrists estimate that about 1 in 100...Ch. R - A game To play a game, you must pay $5 for each...Ch. R - Prob. 4.6RECh. R - Prob. 4.7RECh. R - Prob. 4.8RECh. R - Prob. 4.9RECh. R - Prob. 4.10RECh. R - Prob. 4.11RECh. R - Prob. 4.12RECh. R - Prob. 4.13RECh. R - Prob. 4.14RECh. R - Prob. 4.15RECh. R - R4.17. Stocks Since the stock market began in...Ch. R - Multiple choice A multiple choice test has 50...Ch. R - Prob. 4.18RECh. R - Prob. 4.19RECh. R - Prob. 4.20RECh. R - Prob. 4.21RECh. R - Prob. 4.22RECh. R - Prob. 4.23RECh. R - Prob. 4.24RECh. R - Prob. 4.25RECh. R - Meals A college student on a seven-day meal plan...Ch. R - Prob. 4.27RECh. R - Picking melons Two stores sell watermelons. At the...Ch. R - Prob. 4.29RECh. R - Prob. 4.30RECh. R - Prob. 4.31RECh. R - Prob. 4.32RECh. R - Prob. 4.33RECh. R - Prob. 4.34RECh. R - Prob. 4.35RECh. R - Prob. 4.36RECh. R - Prob. 4.37RECh. R - Prob. 4.38RECh. R - Prob. 4.39RECh. R - Prob. 4.40RECh. R - Prob. 4.41RECh. R - Prob. 4.42RECh. R - Prob. 4.43RECh. R - Prob. 4.44RECh. R - Prob. 5.1RECh. R - Prob. 5.2RECh. R - Prob. 5.3RECh. R - R4.10. Hamsters How large are hamster litters?...Ch. R - Prob. 5.5RECh. R - R4.13. Fake news In a survey of 1002 U.S. adults...Ch. R - Prob. 5.7RECh. R - Prob. 5.8RECh. R - Prob. 5.9RECh. R - Prob. 5.10RECh. R - Prob. 5.11RECh. R - Prob. 5.12RECh. R - Prob. 5.13RECh. R - Prob. 5.14RECh. R - Prob. 5.15RECh. R - R4.27. Language Neurological research has shown...Ch. R - Prob. 5.17RECh. R - Prob. 5.18RECh. R - Prob. 5.19RECh. R - Prob. 5.20RECh. R - Prob. 5.21RECh. R - Prob. 5.22RECh. R - Prob. 5.23RECh. R - Prob. 5.24RECh. R - Prob. 5.25RECh. R - Prob. 5.26RECh. R - Prob. 5.27RECh. R - Prob. 5.28RECh. R - Prob. 5.29RECh. R - Prob. 5.30RECh. R - Prob. 5.31RECh. R - Prob. 5.32RECh. R - Prob. 5.33RECh. R - Prob. 5.34RECh. R - Prob. 5.35RECh. R - Prob. 5.36RECh. R - Prob. 5.37RECh. R - Prob. 5.38RECh. R - Prob. 5.39RECh. R - Prob. 5.40RECh. R - Prob. 6.1RECh. R - Prob. 6.2RECh. R - Prob. 6.3RECh. R - Prob. 6.4RECh. R - Prob. 6.5RECh. R - Prob. 6.6RECh. R - R5.7. Eclampsia deaths Refer again to the research...Ch. R - Prob. 6.8RECh. R - Prob. 6.9RECh. R - Prob. 6.10RECh. R - Prob. 6.11RECh. R - Prob. 6.12RECh. R - Prob. 6.13RECh. R - Prob. 6.14RECh. R - Prob. 6.15RECh. R - Prob. 6.17RECh. R - Prob. 6.18RECh. R - Prob. 6.19RECh. R - Prob. 6.20RECh. R - Prob. 6.21RECh. R - Prob. 6.23RECh. R - Prob. 6.25RECh. R - Prob. 6.28RECh. R - Prob. 6.29RECh. R - Prob. 6.30RECh. R - Prob. 6.31RECh. R - Prob. 6.32RECh. R - Prob. 6.33RECh. R - Prob. 6.34RECh. R - Prob. 6.35RECh. R - Prob. 6.36RECh. R - Prob. 6.37RECh. R - R5.38. Age and party 2016 The Pew Research Center...Ch. R - Prob. 6.39RECh. R - Prob. 6.40RECh. R - Prob. 6.41RECh. R - Prob. 6.42RECh. R - Prob. 6.43RECh. R - Prob. 6.44RECh. R - Prob. 6.45RECh. R - Prob. 6.46RECh. R - Prob. 6.47RECh. R - Prob. 6.48RECh. R - Prob. 6.49RECh. R - R5.50. Cramming Students in two basic Spanish...Ch. R - Prob. 6.51RECh. R - Prob. 6.52RECh. R - Prob. 7.3RECh. R - Prob. 7.4RECh. R - Prob. 7.5RECh. R - Prob. 7.6RECh. R - Prob. 7.7RECh. R - Prob. 7.8RECh. R - Prob. 7.9RECh. R - Prob. 7.10RECh. R - Prob. 7.11RECh. R - Nuclear plants Here are data on 32 light water...Ch. R - Prob. 7.13RECh. R - Prob. 7.15RECh. R - Prob. 7.16RECh. R - Prob. 7.17RECh. R - Prob. 7.18RECh. R - Prob. 7.19RECh. R - Prob. 7.20RECh. R - Prob. 7.21RECh. R - Prob. 7.23RECh. R - Prob. 7.24RECh. R - Prob. 7.25RECh. R - Prob. 7.27RECh. R - Prob. 7.28RECh. R - Prob. 7.29RE
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