Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
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Chapter 12, Problem 38CR
To determine
Check whether the data provide evidence that the proportion of students graduating from colleges and universities in State C for the ethnic group categories differs from the respective proportions in the population for State C.
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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 12 Solutions
Introduction to Statistics and Data Analysis
Ch. 12.1 - A particular cell phone case is available in a...Ch. 12.1 - From the given information in each case below, use...Ch. 12.1 - Prob. 3ECh. 12.1 - The article “In Bronx, Hitting Home Runs Is A...Ch. 12.1 - Prob. 5ECh. 12.1 - The paper Sociochemosensory and Emotional...Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - The report “Fatality Facts 2004: Bicycles”...Ch. 12.1 - Prob. 10E
Ch. 12.1 - Prob. 11ECh. 12.1 - A certain genetic characteristic of a particulai...Ch. 12.1 - Prob. 13ECh. 12.2 - A particular state university system has six...Ch. 12.2 - A random sample of 1000 registered voters in a...Ch. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Can people tell the difference between a female...Ch. 12.3 - The following passage is from the paper Gender...Ch. 12.3 - The article titled Nap Time...Ch. 12.3 - Using data from a national survey, the authors of...Ch. 12 - Each observation in a random sample of 100 bicycle...Ch. 12 - The color vision of birds plays a role in their...Ch. 12 - Prob. 37CRCh. 12 - Prob. 38CRCh. 12 - Prob. 39CRCh. 12 - Prob. 40CRCh. 12 - Prob. 41CRCh. 12 - Prob. 42CRCh. 12 - Prob. 43CRCh. 12 - Prob. 44CR
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