EBK STATISTICAL TECHNIQUES IN BUSINESS
17th Edition
ISBN: 9781259924163
Author: Lind
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 10, Problem 32CE
A recent article in Vitality magazine reported that 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.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 10 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
Ch. 10 - Heinz, a manufacturer of ketchup, uses a...Ch. 10 - Prob. 2SRCh. 10 - For Exercises 14, answer the questions: (a) Is...Ch. 10 - Prob. 2ECh. 10 - Prob. 3ECh. 10 - For Exercises 14, answer the questions: (a) Is...Ch. 10 - For Exercises 58: (a) State the null hypothesis...Ch. 10 - For Exercises 58: (a) State the null hypothesis...Ch. 10 - For Exercises 58: (a) State the null hypothesis...Ch. 10 - For Exercises 58: (a) State the null hypothesis...
Ch. 10 - The mean life of a battery used in a digital clock...Ch. 10 - Given the following hypotheses: H0:10H1:10 A...Ch. 10 - Given the following hypotheses: H0:=400H1:400 A...Ch. 10 - The Rocky Mountain district sales manager of Rath...Ch. 10 - The management of White Industries is considering...Ch. 10 - Prob. 13ECh. 10 - Most air travelers now use e-tickets. Electronic...Ch. 10 - A machine is set to fill a small bottle with 9.0...Ch. 10 - Given the following hypotheses: H0:20H1:20 A...Ch. 10 - Given the following hypotheses: H0:=100H1:100 A...Ch. 10 - The amount of water consumed each day by a healthy...Ch. 10 - The liquid chlorine added to swimming pools to...Ch. 10 - A Washington, D.C., think tank announces the...Ch. 10 - Hugger Polls contends that an agent conducts a...Ch. 10 - Prob. 5SRCh. 10 - Refer to Table 104 and the example just completed....Ch. 10 - Prob. 22ECh. 10 - Prob. 23ECh. 10 - Prob. 24ECh. 10 - According to the local union president, the mean...Ch. 10 - Rutter Nursery Company packages its pine bark...Ch. 10 - A new weight-watching company, Weight Reducers...Ch. 10 - Dole Pineapple Inc. is concerned that the 16-ounce...Ch. 10 - According to a recent survey, Americans get a mean...Ch. 10 - A statewide real estate sales agency, Farm...Ch. 10 - According to the Census Bureau, 3.13 people reside...Ch. 10 - A recent article in Vitality magazine reported...Ch. 10 - Prob. 33CECh. 10 - Prob. 34CECh. 10 - A recent study revealed the typical American...Ch. 10 - The postanesthesia care area (recovery room) at...Ch. 10 - www.golfsmith.com receives an average of 6.5...Ch. 10 - During recent seasons, Major League Baseball has...Ch. 10 - Watch Corporation of Switzerland claims that its...Ch. 10 - Listed below is the annual rate of return...Ch. 10 - Many grocery stores and large retailers such as...Ch. 10 - For a recent year, the mean fare to fly from...Ch. 10 - The publisher of Celebrity Living claims that the...Ch. 10 - A United Nations report shows the mean family...Ch. 10 - Prob. 45CECh. 10 - The American Water Works Association reports that...Ch. 10 - A cola-dispensing machine is set to dispense 9.00...Ch. 10 - The owners of the Westfield Mall wished to study...Ch. 10 - The following null and alternate hypotheses are...Ch. 10 - An insurance company, based on past experience,...Ch. 10 - A national grocers magazine reports the typical...Ch. 10 - Prob. 52DACh. 10 - Refer to the Lincolnville School District bus...
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