INTRODUCTION TO STATISTICS & DATA ANALYS
6th Edition
ISBN: 9780357420447
Author: PECK
Publisher: CENGAGE L
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Chapter 1.4, Problem 15E
For the following numerical variables, state whether each is discrete or continuous.
- a. The length of a 1-year-old rattlesnake
- b. The altitude of a location in California selected randomly by throwing a dart at a map of the state
- c. The distance from the left edge at which a 12-inch plastic ruler snaps when bent sufficiently to break
- d. The price per gallon paid by the next customer to buy gas at a particular station
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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 1 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
Ch. 1.3 - Give brief definitions of the terms descriptive...Ch. 1.3 - Give brief definitions of the terms population and...Ch. 1.3 - The following conclusion from a study appeared in...Ch. 1.3 - Based on a study of 2 121 children between the...Ch. 1.3 - The student senate at a university with 15,000...Ch. 1.3 - The National Retail Federation used data from a...Ch. 1.3 - The supervisors of a rural county are interested...Ch. 1.3 - A consumer group conducts crash tests of new model...Ch. 1.3 - A building contractor has a chance to buy an odd...Ch. 1.3 - The article Brain Shunt Tested to Treat Alzheimers...
Ch. 1.3 - In a study of whether taking a garlic supplement...Ch. 1.4 - Classify each of the following variables as either...Ch. 1.4 - Classify each of the following variables as either...Ch. 1.4 - For the following numerical variables, state...Ch. 1.4 - For the following numerical variables, state...Ch. 1.4 - For each of the following situations, give a set...Ch. 1.4 - In a survey of 100 people who had recently...Ch. 1.4 - The Gallup report More Americans Say Real Estate...Ch. 1.4 - An article in the New Times San Luis Obispo...Ch. 1.4 - Box Office Mojo (boxofficemojo.com) tracks movie...Ch. 1.4 - The report With Their Whole Lives Ahead of Them...Ch. 1.4 - The following display is a graph similar to one...Ch. 1.4 - The accompanying table gives the total number...Ch. 1.4 - Heal the Bay is an environmental organization that...Ch. 1.4 - The report referenced in the previous exercise...Ch. 1.4 - The U.S. Department of Health and Human Services...Ch. 1.4 - Example 1.5 gave the accompanying data on violent...Ch. 1.4 - The article Fliers Trapped on Tarmac Push for...Ch. 1.4 - The report Trends m Community Colleges...Ch. 1.4 - The article Where College Students Buy Textbooks...Ch. 1.4 - Prob. 31ECh. 1.4 - In the United States, movies are rated by the...Ch. 1 - The report Testing the Waters 2009 (nrdc.org)...Ch. 1 - The U.S. Department of Education reported that 14%...Ch. 1 - The Computer Assisted Assessment Center at the...Ch. 1 - The article Just How Safe Is That Jet? (USA TODAY,...Ch. 1 - Each year, U.S. News and World Report publishes a...Ch. 1 - Many adolescent boys aspire to be professional...
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