Basic Business Statistics Student Value Edition Plus NEW MyLab Statistics with Pearson eText -- Access Card Package (13th Edition)
13th Edition
ISBN: 9780133873641
Author: Mark L. Berenson, David M. Levine, Kathryn A. Szabat
Publisher: PEARSON
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Chapter 7, Problem 21PS
Why does the sampling distribution of the
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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 7 Solutions
Basic Business Statistics Student Value Edition Plus NEW MyLab Statistics with Pearson eText -- Access Card Package (13th Edition)
Ch. 7 - Given a normal distribution with =100and=10, if...Ch. 7 - Given a normal distribution with =50and=5, if you...Ch. 7 - For each of the following three populations,...Ch. 7 - The following data represent the number of days...Ch. 7 - The diameter of a brand of tennis balls is...Ch. 7 - Prob. 6PSCh. 7 - According to a mashable post. time spent on...Ch. 7 - Today, full-time college students report spending...Ch. 7 - In a random sample of 64 people, 48 are classified...Ch. 7 - A random sample of 50 households was selected for...
Ch. 7 - The following data represent the responses (Y for...Ch. 7 - A political pollster is conducting an analysis of...Ch. 7 - You plan to conduct a marketing experiment in...Ch. 7 - Prob. 14PSCh. 7 - Prob. 15PSCh. 7 - Prob. 16PSCh. 7 - The Chartered Financial Analyst (CFA) institute...Ch. 7 - A Pew Research Center project on the state of news...Ch. 7 - Why is the sample mean an unbiased estimator of...Ch. 7 - Why does the standard error of the mean decrease...Ch. 7 - Why does the sampling distribution of the mean...Ch. 7 - What is the difference between a population...Ch. 7 - Under what circumstances does the sampling...Ch. 7 - An industrial sewing machine uses ball bearings...Ch. 7 - The fill amount of bottles of a soft drinks is...Ch. 7 - Prob. 26PSCh. 7 - In Problem 7.26, suppose that the mean amount of...Ch. 7 - Prob. 28PSCh. 7 - Prob. 29PS
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