Statistics (13th Edition)
13th Edition
ISBN: 9780134080215
Author: James T. McClave, Terry T Sincich
Publisher: PEARSON
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Chapter 14.5, Problem 60UP
To determine
Identify the results that would lead to conclusion that the treatments in a balanced, completely randomized design have distributions that differ in location.
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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 14 Solutions
Statistics (13th Edition)
Ch. 14.2 - Prob. 1UPCh. 14.2 - Prob. 2UPCh. 14.2 - Prob. 3LMCh. 14.2 - Prob. 4LMCh. 14.2 - Prob. 5LMCh. 14.2 - Music performance anxiety. Refer to the British...Ch. 14.2 - Prob. 7ACBCh. 14.2 - 15.8 Caffeine in Starbucks coffee. Researchers at...Ch. 14.2 - Emotional empathy in young adults. Refer to the...Ch. 14.2 - Prob. 10ACB
Ch. 14.2 - Prob. 11ACBCh. 14.2 - Prob. 12ACICh. 14.2 - 15.10 Lobster trap placement. Refer to the...Ch. 14.2 - Prob. 14ACICh. 14.2 - Prob. 15ACICh. 14.2 - Prob. 16ACICh. 14.2 - Prob. 17ACICh. 14.3 - What is a rank sum?
Ch. 14.3 - Prob. 19UPCh. 14.3 - Prob. 20UPCh. 14.3 - Prob. 21LMCh. 14.3 - 15.17 Suppose you want to compare two treatments,...Ch. 14.3 - Prob. 23LMCh. 14.3 - Random samples of sizes n1 = 16 and n2 = 12 were...Ch. 14.3 - 15.18 Independent random samples are selected from...Ch. 14.3 - Prob. 26ACBCh. 14.3 - Prob. 27ACBCh. 14.3 - Prob. 28ACBCh. 14.3 - 15.23 The X-Factor in golf performance. Many golf...Ch. 14.3 - Prob. 30ACBCh. 14.3 - Prob. 31ACBCh. 14.3 - 15.85 Children’s recall of TV ads. Refer to the...Ch. 14.3 - Prob. 33ACICh. 14.3 - Prob. 34ACICh. 14.3 - Prob. 35ACICh. 14.3 - Prob. 36ACICh. 14.3 - Prob. 37ACICh. 14.3 - Prob. 38ACICh. 14.3 - Prob. 39ACICh. 14.4 - Explain the difference between the one- and...Ch. 14.4 - Prob. 41UPCh. 14.4 - Prob. 42LMCh. 14.4 - Prob. 43LMCh. 14.4 - Prob. 44LMCh. 14.4 - Prob. 45LMCh. 14.4 - A random sample of nine pairs of measurements is...Ch. 14.4 - Prob. 47ACBCh. 14.4 - Prob. 48ACBCh. 14.4 - Prob. 49ACBCh. 14.4 - Prob. 50ACBCh. 14.4 - Reading comprehension strategies of elementary...Ch. 14.4 - Prob. 52ACBCh. 14.4 - Prob. 53ACICh. 14.4 - Prob. 54ACICh. 14.4 - Prob. 55ACICh. 14.4 - Neurological impairment of POWs. Eleven prisoners...Ch. 14.4 - Prob. 57ACICh. 14.4 - Prob. 58ACACh. 14.5 - 15.43 Under what circumstances does the χ2...Ch. 14.5 - Which of the following results would lead you to...Ch. 14.5 - Suppose you want to use the Kruskal-Wallis H-test...Ch. 14.5 - Data were collected from three populations—A, B...Ch. 14.5 - 15.46 Containing wildfires. The International...Ch. 14.5 - 15.47 Road safety of neighborhoods. The Canadian...Ch. 14.5 - Dog behavior on walks. A field study was conducted...Ch. 14.5 - 15.49 Improving driving performance while...Ch. 14.5 - Effect of scopolamine on memory. Refer to the...Ch. 14.5 - 15.48 Commercial eggs produced from different...Ch. 14.5 - 15.50 Relieving pain with hypnosis. Rehabilitation...Ch. 14.5 - Energy expenditure of laughter. Refer to the...Ch. 14.5 -
Restoring self-control when intoxicated. Refer...Ch. 14.5 - Ground water contamination of wells. Refer to the...Ch. 14.5 - The “name game.” Refer to the Journal of...Ch. 14.5 -
Is honey a cough remedy? Refer to the Archives...Ch. 14.6 - Which of the following statements correctly...Ch. 14.6 - What conditions are required for a valid...Ch. 14.6 - Data were collected under a randomized block...Ch. 14.6 - 15.55 Suppose you have used a randomized block...Ch. 14.6 - 15.56 An experiment was conducted using a...Ch. 14.6 - A new method of evaluating health care research...Ch. 14.6 - Prob. 81ACBCh. 14.6 - 15.64 Containers designed to cool citrus fruit....Ch. 14.6 - 15.57 Estimating time needed to complete a task....Ch. 14.6 - 15.60 Taste testing scales. Refer to the Journal...Ch. 14.6 - Impact study of distractions while driving. The...Ch. 14.6 - 15.58 Condit ions impeding farm production. A...Ch. 14.6 - “Topsy-turvy” seasons in college football. Refer...Ch. 14.6 - 15.65 Irrelevant facial similarity effects on...Ch. 14.6 - Effect of massage on boxers. Refer to the British...Ch. 14.6 - Plants and stress reduction. Refer to the Kansas...Ch. 14.7 - What is the value of rS when there is perfect...Ch. 14.7 - What conditions are required for a valid...Ch. 14.7 - 15.66 Use Table XIV at the end of this chapter to...Ch. 14.7 - 15.67 Specify the rejection region for Spearman’s...Ch. 14.7 - 15.69 Compute Spearman s rank correlation...Ch. 14.7 - 15.68 The following sample data were collected on...Ch. 14.7 - Measuring the moon’s orbit. Refer to the American...Ch. 14.7 - Mongolian desert ants. Refer to the Journal of...Ch. 14.7 - Game performance of water polo players. Refer to...Ch. 14.7 - Lobster fishing study. Refer to the Bulletin of...Ch. 14.7 - Effect of massage on boxers. Refer to the British...Ch. 14.7 - Childhood obesity study. Refer to the Journal of...Ch. 14.7 - Groundwater contamination of wells. Refer to the...Ch. 14.7 - The “name game.” Refer to the Journal of...Ch. 14.7 - 15.76 Taste testing scales. Refer to the Journal...Ch. 14.7 - 15.75 In business, do nice guys finish first or...Ch. 14.7 - 15.74 Food availability at middle schools. Refer...Ch. 14.7 - Pain empathy and brain activity. Refer to the...Ch. 14.7 - Public perceptions of health risks. Refer to the...Ch. 14 - Prob. 110UPCh. 14 - For each of the following, give the appropriate...Ch. 14 - 15.80 The data for three independent random...Ch. 14 - 15.81 A random sample of nine pairs of...Ch. 14 - 15.82 Two independent random samples produced the...Ch. 14 - 15.83 An experiment was conducted using a...Ch. 14 - Radioactive lichen. Refer to the Lichen...Ch. 14 - Prob. 118ACBCh. 14 - Prob. 119ACBCh. 14 - Prob. 120ACBCh. 14 - Prob. 121ACBCh. 14 - Extending the life of an aluminum smelter pot....Ch. 14 - 15.36 NHTSA new car crash tests. Refer to the...Ch. 14 - Prob. 124ACICh. 14 - Prob. 125ACICh. 14 - Prob. 126ACICh. 14 - Prob. 127ACICh. 14 - Prob. 128ACICh. 14 - Prob. 129ACICh. 14 - Prob. 130ACICh. 14 - Prob. 131ACICh. 14 - Prob. 132ACICh. 14 - Prob. 133ACICh. 14 - Prob. 134ACICh. 14 - Prob. 135ACICh. 14 - Prob. 136ACICh. 14 - Prob. 137ACICh. 14 - Prob. 138CTC
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