Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 1, Problem 1.21CE
Roger Amster teaches an English course in which 40 students are enrolled. After yesterday’s class, Roger questioned the 5 students who always sit in the back of the classroom. Three of the 5 said “yes” when asked if they would like A Tale of Two Cities as the next class reading assignment.
a. Identify the population and the sample in this situation.
b. Is this likely to be a representative sample? If not, why not?
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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 Business Statistics
Ch. 1.2 - What was the primary use of statistics in ancient...Ch. 1.2 - what ways can business statistics be useful in...Ch. 1.3 - What is the difference between descriptive...Ch. 1.3 - In 2008, Piedmont Natural Gas Corporation sold...Ch. 1.3 - An article in a fitness magazine described a study...Ch. 1.4 - What is the difference between a qualitative...Ch. 1.4 - What is the difference between discrete and...Ch. 1.4 - The Acme School of Locksmithing has been...Ch. 1.4 - Jeff Rowlen, a labor relations expert, has...Ch. 1.4 - The Snowbird Ski Lodge attracts skiers from...
Ch. 1.5 - Restaurants sometimes provide “customer reaction”...Ch. 1.5 - What kinds of statistical data might a burglar...Ch. 1.6 - The text claims that a company or organization...Ch. 1.6 - The headline of an article in your daily newspaper...Ch. 1 - A research firm observes that men are twice as...Ch. 1 - For each of the following, indicate whether the...Ch. 1 - What kinds of statistical data play a role in an...Ch. 1 - For each of the following, indicate the scale of...Ch. 1 - Most undergraduate business students will not go...Ch. 1 - Bill scored 1200 on the Scholastic Aptitude Test...Ch. 1 - Roger Amster teaches an English course in which 40...Ch. 1 - In studying the performance of the company’s stock...
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