EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
7th Edition
ISBN: 9780136961888
Author: Triola
Publisher: PEARSON CO
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Chapter 6, Problem 7CQQ
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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.
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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 + €
•
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.
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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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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 6 Solutions
EP ELEMENTARY STAT.USING EXC.-MYSTATLAB
Ch. 6.1 - 1. Normal Distribution What’s wrong with the...Ch. 6.1 - Prob. 2BSCCh. 6.1 - Prob. 3BSCCh. 6.1 - Prob. 4BSCCh. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Prob. 7BSCCh. 6.1 - Prob. 8BSCCh. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...
Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Prob. 17BSCCh. 6.1 - Prob. 18BSCCh. 6.1 - Prob. 19BSCCh. 6.1 - Prob. 20BSCCh. 6.1 - Prob. 21BSCCh. 6.1 - Prob. 22BSCCh. 6.1 - Prob. 23BSCCh. 6.1 - Prob. 24BSCCh. 6.1 - Prob. 25BSCCh. 6.1 - Prob. 26BSCCh. 6.1 - Prob. 27BSCCh. 6.1 - Prob. 28BSCCh. 6.1 - Prob. 29BSCCh. 6.1 - Prob. 30BSCCh. 6.1 - Prob. 31BSCCh. 6.1 - Prob. 32BSCCh. 6.1 - Prob. 33BSCCh. 6.1 - Prob. 34BSCCh. 6.1 - Prob. 35BSCCh. 6.1 - Prob. 36BSCCh. 6.1 - Finding Bone Density Scores. In Exercises 37–40...Ch. 6.1 - Prob. 38BSCCh. 6.1 - Prob. 39BSCCh. 6.1 - Prob. 40BSCCh. 6.1 - Prob. 41BSCCh. 6.1 - Prob. 42BSCCh. 6.1 - Prob. 43BSCCh. 6.1 - Prob. 44BSCCh. 6.1 - Prob. 45BSCCh. 6.1 - Prob. 46BSCCh. 6.1 - Prob. 47BSCCh. 6.1 - Prob. 48BSCCh. 6.1 - Prob. 49BBCh. 6.1 - Prob. 50BBCh. 6.2 - Prob. 1BSCCh. 6.2 - Prob. 2BSCCh. 6.2 - Prob. 3BSCCh. 6.2 - Prob. 4BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - Prob. 7BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - Prob. 11BSCCh. 6.2 - Prob. 12BSCCh. 6.2 - Prob. 13BSCCh. 6.2 - Prob. 14BSCCh. 6.2 - Prob. 15BSCCh. 6.2 - Prob. 16BSCCh. 6.2 - Prob. 17BSCCh. 6.2 - Prob. 18BSCCh. 6.2 - Prob. 19BSCCh. 6.2 - Prob. 20BSCCh. 6.2 - Prob. 21BSCCh. 6.2 - Prob. 22BSCCh. 6.2 - Prob. 23BSCCh. 6.2 - Prob. 24BSCCh. 6.2 - Prob. 25BSCCh. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - Prob. 28BSCCh. 6.2 - Prob. 29BSCCh. 6.2 - Prob. 30BSCCh. 6.2 - Prob. 31BSCCh. 6.2 - Prob. 32BSCCh. 6.2 - Prob. 33BSCCh. 6.2 - Prob. 34BSCCh. 6.2 - Prob. 35BSCCh. 6.2 - Prob. 36BSCCh. 6.2 - Prob. 37BBCh. 6.2 - Prob. 38BBCh. 6.3 - Prob. 1BSCCh. 6.3 - Prob. 2BSCCh. 6.3 - Prob. 3BSCCh. 6.3 - Prob. 4BSCCh. 6.3 - Prob. 5BSCCh. 6.3 - Prob. 6BSCCh. 6.3 - Prob. 7BSCCh. 6.3 - Prob. 8BSCCh. 6.3 - Prob. 9BSCCh. 6.3 - In Exercises 7–10, use the same population of {4,...Ch. 6.3 - Prob. 11BSCCh. 6.3 - Prob. 12BSCCh. 6.3 - Prob. 13BSCCh. 6.3 - Prob. 14BSCCh. 6.3 - Prob. 15BSCCh. 6.3 - Prob. 16BSCCh. 6.3 - Prob. 17BSCCh. 6.3 - Prob. 18BSCCh. 6.3 - Prob. 19BBCh. 6.3 - Prob. 20BBCh. 6.4 - Prob. 1BSCCh. 6.4 - Prob. 2BSCCh. 6.4 - Prob. 3BSCCh. 6.4 - Prob. 4BSCCh. 6.4 - Prob. 5BSCCh. 6.4 - Prob. 6BSCCh. 6.4 - Prob. 7BSCCh. 6.4 - Prob. 8BSCCh. 6.4 - Prob. 9BSCCh. 6.4 - Prob. 10BSCCh. 6.4 - Prob. 11BSCCh. 6.4 - Prob. 12BSCCh. 6.4 - Prob. 13BSCCh. 6.4 - Prob. 14BSCCh. 6.4 - Prob. 15BSCCh. 6.4 - Prob. 16BSCCh. 6.4 - Prob. 17BSCCh. 6.4 - Prob. 18BSCCh. 6.4 - Prob. 19BSCCh. 6.4 - Prob. 20BBCh. 6.5 - Prob. 1BSCCh. 6.5 - Prob. 2BSCCh. 6.5 - Prob. 3BSCCh. 6.5 - Prob. 4BSCCh. 6.5 - Prob. 5BSCCh. 6.5 - Prob. 6BSCCh. 6.5 - Prob. 7BSCCh. 6.5 - Prob. 8BSCCh. 6.5 - Prob. 9BSCCh. 6.5 - Prob. 10BSCCh. 6.5 - Prob. 11BSCCh. 6.5 - Prob. 12BSCCh. 6.5 - Prob. 13BSCCh. 6.5 - Prob. 14BSCCh. 6.5 - Prob. 15BSCCh. 6.5 - Prob. 16BSCCh. 6.5 - Prob. 17BSCCh. 6.5 - Prob. 18BSCCh. 6.5 - Prob. 19BSCCh. 6.5 - Prob. 20BSCCh. 6.5 - Prob. 21BBCh. 6.5 - Prob. 22BBCh. 6 - Prob. 1CQQCh. 6 - Prob. 2CQQCh. 6 - Prob. 3CQQCh. 6 - Prob. 4CQQCh. 6 - Prob. 5CQQCh. 6 - Prob. 6CQQCh. 6 - Prob. 7CQQCh. 6 - Prob. 8CQQCh. 6 - Prob. 9CQQCh. 6 - Prob. 10CQQCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 1CRECh. 6 - Prob. 2CRECh. 6 - Prob. 3CRECh. 6 - Prob. 4CRECh. 6 - Prob. 5CRECh. 6 - Prob. 1FDD
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