Essential Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781506386300
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 7, Problem 27CAP
To determine
To explain why we restrict alpha from being larger than
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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
Essential Statistics for the Behavioral Sciences
Ch. 7 - Prob. 1FPCh. 7 - Prob. 2FPCh. 7 - Prob. 3FPCh. 7 - Prob. 4FPCh. 7 - Prob. 5FPCh. 7 - Prob. 6FPCh. 7 - Prob. 7FPCh. 7 - Prob. 8FPCh. 7 - Prob. 9FPCh. 7 - Prob. 10FP
Ch. 7 - Prob. 11FPCh. 7 - Prob. 12FPCh. 7 - Prob. 13CAPCh. 7 - Prob. 14CAPCh. 7 - Prob. 15CAPCh. 7 - Prob. 16CAPCh. 7 - Prob. 17CAPCh. 7 - Prob. 18CAPCh. 7 - Prob. 19CAPCh. 7 - Prob. 20CAPCh. 7 - Prob. 21CAPCh. 7 - Prob. 22CAPCh. 7 - Prob. 23CAPCh. 7 - Prob. 24CAPCh. 7 - Prob. 25CAPCh. 7 - Prob. 26CAPCh. 7 - Prob. 27CAPCh. 7 - Prob. 28CAPCh. 7 - Prob. 29PRCh. 7 - Prob. 30PRCh. 7 - Prob. 31PRCh. 7 - Prob. 32PRCh. 7 - Prob. 33PRCh. 7 - Prob. 34PR
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