UNDERSTANDING BASIC STAT LL BUND >A< F
7th Edition
ISBN: 9781337372763
Author: BRASE
Publisher: Cengage Learning
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Chapter 3.1, Problem 13P
Critical Thinking Consider the numbers
23455
(a) Compute the
(b) If the numbers represent codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense?
(c) If the numbers represent one-way mileages for trails to different lakes. which average(s) would nuke sense?
(d) Suppose the numbers represent survey responses from 1 to 5, with 1 = disagree strongly, 2 = disagree, 3 = agree, 4 = agree strongly, and 5 = agree very strongly. Which averages make sense?
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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
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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].
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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 3 Solutions
UNDERSTANDING BASIC STAT LL BUND >A< F
Ch. 3.1 - Statistical Literacy Consider the mode, median,...Ch. 3.1 - Statistical Literacy What symbol is used for the...Ch. 3.1 - Statistical Literacy Look at the formula for the...Ch. 3.1 - Statistical Literacy In order to find the median...Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Basic Computations Mean, Median, Mode Find the...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking If a data set has an even number...
Ch. 3.1 - Critical Thinking When a distribution is...Ch. 3.1 - Critical Thinking Consider the following types of...Ch. 3.1 - Critical Thinking Consider the numbers 23455 (a)...Ch. 3.1 - Critical Thinking Consider two data sets. Set...Ch. 3.1 - Interpretation A Job-performance evaluation form...Ch. 3.1 - Critical Thinking: Data Transformation Using...Ch. 3.1 - Critical Thinking: Data Transformation Using...Ch. 3.1 - Critical Thinking Consider a data set of 15...Ch. 3.1 - Environmental Studies: Death Valley How hot does...Ch. 3.1 - Ecology: Wolf Packs How large is a wolf pack? The...Ch. 3.1 - Medical: Injuries The Grand Canyon and the...Ch. 3.1 - Football: Age of Professional Players How old are...Ch. 3.1 - Prob. 23PCh. 3.1 - Basic Computation: Weighted Average Find the...Ch. 3.1 - Basic Computation: Weighted Average Find the...Ch. 3.1 - Grades: Weighted Average In your biology class,...Ch. 3.1 - Merit Pay Scale: Weighted Average At General...Ch. 3.1 - EPA: Wetlands Where does all the water go?...Ch. 3.1 - Expand Your knowledge: Harmonic Mean When data...Ch. 3.1 - Expand Your Knowledge: Geometric Mean When data...Ch. 3.2 - Statistical Literacy Which averagemean, median, or...Ch. 3.2 - Statistical Literacy What is the relationship...Ch. 3.2 - Statistical Literacy When computing the standard...Ch. 3.2 - Statistical Literary What symbol is used for the...Ch. 3.2 - Basic Computation: Range, Standard Deviation...Ch. 3.2 - Basic Computation: Range, Standard Deviation...Ch. 3.2 - Critical Thinking Fora given data set in which not...Ch. 3.2 - Critical Thinking Consider two data sets with...Ch. 3.2 - Critical Thinking Each of the following data sets...Ch. 3.2 - Critical Thinking: Data Transformation Using...Ch. 3.2 - Critical Thinking: Data Transformation Using...Ch. 3.2 - Critical Thinking: Outliers One indicator of an...Ch. 3.2 - Basic Computation: Variance, Standard Deviation...Ch. 3.2 - Basic Computation: Coefficient of Variation,...Ch. 3.2 - Basic Computation: Coefficient of Variation....Ch. 3.2 - Investing: Stocks and Bonds Do bonds reduce the...Ch. 3.2 - Space Shuttle: Epoxy Kevlar epoxy it a material...Ch. 3.2 - Archaeology: Ireland The Hill of Tara in Ireland...Ch. 3.2 - Wildlife: Mallard Ducks and Canada Geese For...Ch. 3.2 - Investing: Socially Responsible Mutual Funds Pax...Ch. 3.2 - Medical: Physician Visits In some reports, the...Ch. 3.2 - Grouped Data: Anthropology What was the age...Ch. 3.2 - Grouped Data: Shoplifting What is the age...Ch. 3.2 - Grouped Data: Hours of Sleep per Day Alexander...Ch. 3.2 - Grouped Data: Business Administration What are the...Ch. 3.2 - Prob. 26PCh. 3.2 - Prob. 27PCh. 3.2 - Expand Your knowledge: Stratified Sampling and...Ch. 3.2 - Expand Your knowledge: Stratified Sampling and...Ch. 3.2 - Prob. 30PCh. 3.3 - Statistical Literacy Angela took a general...Ch. 3.3 - Statistical Literacy One standard for admission to...Ch. 3.3 - Critical Thinking The town of Butler, Nebraska,...Ch. 3.3 - Critical Thinking Clayton and Timothy took...Ch. 3.3 - Basic Computation: Five-Number Summary,...Ch. 3.3 - Basic Computation: Five-Number Summary...Ch. 3.3 - Health Care: Nurses At Center Hospital there is...Ch. 3.3 - Health Care: Staff Another survey was done at...Ch. 3.3 - Sociology: College Graduates What percentage of...Ch. 3.3 - Sociology: High School Dropouts What percentage of...Ch. 3.3 - Auto Insurance: Interpret GraphsConsumer Reports...Ch. 3.3 - Expand Your knowledge: Outliers Some data include...Ch. 3 - Statistical Literacy (a) What measures of...Ch. 3 - Critical Thinking Look at the two histograms on...Ch. 3 - Critical Thinking Consider the following Minitab...Ch. 3 - Prob. 4CRCh. 3 - Political Science: Georgia Democrats How...Ch. 3 - Grade: Weighted Average Professor Cramer...Ch. 3 - General: Average Weight Wright An elevator it...Ch. 3 - Agriculture: Harvest Weight of Maize The following...Ch. 3 - Focus Problem: Water Solve the focus problem at...Ch. 3 - Agriculture: Bell Peppers The pathogen...Ch. 3 - Performance Rating: Weighted Average A performance...Ch. 3 - The Story of Old Faithful is a short book written...Ch. 3 - Most academic advisors tell students to major in a...Ch. 3 - An average is an attempt to summarize a collection...Ch. 3 - Why do we need to study the variation of a...Ch. 3 - Why is the coefficient of variation important?...Ch. 3 - What is Chebyshevs theorem? Suppose you have a...Ch. 3 - Application Using the software or calculator...Ch. 3 - Consider the following measures: mean, median,...Ch. 3 - Describe how the presence of possible outliers...Ch. 3 - Consider two data sets. A and B. The sets are...Ch. 3 - You are examining two data sets involving test...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - In west Texas, water is extremely important. The...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...Ch. 3 - Interpretation Wow! In Problems 5-13 you...
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