MyLab Statistics with Pearson eText -- Standalone Access Card -- for Fundamentals of Statistics
5th Edition
ISBN: 9780134743295
Author: Michael III Sullivan
Publisher: PEARSON
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Chapter 2.2, Problem 7AYU
True or False: The shape of the distribution shown is best classified as skewed left.
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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.
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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 2 Solutions
MyLab Statistics with Pearson eText -- Standalone Access Card -- for Fundamentals of Statistics
Ch. 2.1 - Define raw data in your own words.Ch. 2.1 - A frequency distribution lists the _____ of...Ch. 2.1 - In a relative frequency distribution, what should...Ch. 2.1 - What is a bar graph? What is a Pareto chart?Ch. 2.1 - Flu Season The pie chart shown, the type we see in...Ch. 2.1 - Cosmetic Surgery This USA Today type chart shows...Ch. 2.1 - Most Valuable Player The following Pareto chart...Ch. 2.1 - Poverty The U.S. Census Bureau uses money income...Ch. 2.1 - Divorce The following graph represents the results...Ch. 2.1 - Identity Theft Identity fraud occurs when someone...
Ch. 2.1 - Made in America A random sample of 2163 adults...Ch. 2.1 - Desirability Attributes A random sample of 2163...Ch. 2.1 - College Survey In a national survey conducted by...Ch. 2.1 - College Survey In a national survey conducted by...Ch. 2.1 - Use the Internet? The Gallup organization...Ch. 2.1 - Dining Out A sample of 521 adults was asked, How...Ch. 2.1 - NW Texting A survey of U.S. adults and teens (ages...Ch. 2.1 - Educational Attainment The educational attainment...Ch. 2.1 - Dream Job A survey of adult men and women asked,...Ch. 2.1 - Car Color A survey of 100 randomly selected autos...Ch. 2.1 - Prob. 21AYUCh. 2.1 - Bachelor Party In a survey conducted by Opinion...Ch. 2.1 - Favorite Day to Eat Out A survey was conducted by...Ch. 2.1 - Prob. 25AYUCh. 2.1 - Prob. 26AYUCh. 2.1 - Prob. 27AYUCh. 2.1 - StatCrunch Survey Choose a qualitative variable...Ch. 2.1 - Putting It Together: Online Homework Keeping...Ch. 2.1 - When should relative frequencies be used when...Ch. 2.1 - Prob. 31AYUCh. 2.1 - Prob. 32AYUCh. 2.1 - Prob. 33AYUCh. 2.2 - The categories by which data are grouped are...Ch. 2.2 - The _____ class limit is the smallest value within...Ch. 2.2 - The _____ is the difference between consecutive...Ch. 2.2 - Prob. 4AYUCh. 2.2 - Prob. 5AYUCh. 2.2 - Prob. 6AYUCh. 2.2 - True or False: The shape of the distribution shown...Ch. 2.2 - Prob. 8AYUCh. 2.2 - Rolling the Dice An experiment was conducted in...Ch. 2.2 - Car Sales A car salesman records the number of...Ch. 2.2 - IQ Scores The following frequency histogram...Ch. 2.2 - Alcohol-Related Traffic Fatalities The frequency...Ch. 2.2 - In Problems 13 and 14, for each variable...Ch. 2.2 - In Problems 13 and 14, for each variable...Ch. 2.2 - Misery Index The following time-series plot shows...Ch. 2.2 - Prob. 16AYUCh. 2.2 - Predicting School Enrollment To predict future...Ch. 2.2 - Free Throws In an experiment, a researcher asks a...Ch. 2.2 - In Problems 1922, determine the original set of...Ch. 2.2 - In Problems 1922, determine the original set of...Ch. 2.2 - In Problems 1922, determine the original set of...Ch. 2.2 - In Problems 1922, determine the original set of...Ch. 2.2 - find (a) the number of classes, (b) the class...Ch. 2.2 - Earthquakes The following data represent the...Ch. 2.2 - In Problems 25 and 26, construct (a) a relative...Ch. 2.2 - In Problems 25 and 26, construct (a) a relative...Ch. 2.2 - NW Televisions in the Household A researcher with...Ch. 2.2 - Waiting The data below represent the number of...Ch. 2.2 - NW Gini Index The Gini Index is a measure of how...Ch. 2.2 - Average Income The following data represent the...Ch. 2.2 - Cigarette Tex Rates The table shows the tax, in...Ch. 2.2 - Dividend Yield A dividend is a payment from a...Ch. 2.2 - NW Violent Crimes Violent crimes include murder,...Ch. 2.2 - Volume of Altria Group Stock The volume of a stock...Ch. 2.2 - Prob. 35AYUCh. 2.2 - Prob. 36AYUCh. 2.2 - Prob. 37AYUCh. 2.2 - Prob. 38AYUCh. 2.2 - Prob. 39AYUCh. 2.2 - Prob. 40AYUCh. 2.2 - NW Violent Crimes Use the violent crime rate data...Ch. 2.2 - Academy Award Winners The following data represent...Ch. 2.2 - Prob. 43AYUCh. 2.2 - Sullivan Survey Choose a continuous quantitative...Ch. 2.2 - Prob. 46AYUCh. 2.2 - Prob. 47AYUCh. 2.2 - Waiting Draw a dot plot of the waiting data from...Ch. 2.2 - Prob. 49AYUCh. 2.2 - Prob. 50AYUCh. 2.2 - Prob. 51AYUCh. 2.2 - Prob. 52AYUCh. 2.2 - Prob. 53AYUCh. 2.2 - Putting It Together: Which Graphical Summary?...Ch. 2.2 - Prob. 55AYUCh. 2.2 - Prob. 56AYUCh. 2.2 - Discuss the advantages and disadvantages of...Ch. 2.2 - Prob. 58AYUCh. 2.2 - Describe the situations in which it is preferable...Ch. 2.2 - Sketch four histogramsone skewed right, one skewed...Ch. 2.2 - What type of variable is required when drawing...Ch. 2.3 - Inauguration Cost The following is a USA...Ch. 2.3 - Burning Calories The following is a USA Today-type...Ch. 2.3 - NW Median Earnings The graph shows the median...Ch. 2.3 - Union Membership The following relative frequency...Ch. 2.3 - NW Robberies A newspaper article claimed that the...Ch. 2.3 - Car Accidents An article in a student newspaper...Ch. 2.3 - Tax Revenue The following histogram drawn in...Ch. 2.3 - You Explain It! Oil Reserves The U.S. Strategic...Ch. 2.3 - NW Cost of Kids The following is a USA Today-type...Ch. 2.3 - Worker Injury The safety manager at Klutz...Ch. 2.3 - Health Care Expenditures The following data...Ch. 2.3 - Prob. 12AYUCh. 2.3 - NW Overweight Between 1980 and 2012, the number of...Ch. 2.3 - Ideal Family Size The following USA Today-type...Ch. 2.3 - National League Baseball MVP The following pie...Ch. 2.3 - Prob. 16AYUCh. 2 - Effective Commercial Harris Interactive conducted...Ch. 2 - Weapons Used in Homicide The following frequency...Ch. 2 - Live Births The following frequency distribution...Ch. 2 - Political Affiliation One hundred randomly...Ch. 2 - Family Size A random sample of 60 couples married...Ch. 2 - Home Ownership Rates The table shows the home...Ch. 2 - Diameter of a Cookie The following data represent...Ch. 2 - Time Online The following data represent the...Ch. 2 - Grade Inflation The side-by-side bar graph to the...Ch. 2 - Income Distribution The following data represent...Ch. 2 - Misleading Graphs In 2013, the average earnings of...Ch. 2 - High Heels The graphic to the right is a USA Today...Ch. 2 - The graph shows the ratings on Yelp for Hot Dougs...Ch. 2 - A random sample of 1005 adult Americans was asked,...Ch. 2 - Interested in knowing the educational background...Ch. 2 - The following data represent the number of cars...Ch. 2 - Dr. Paul Oswiecmiski randomly selects 40 of his...Ch. 2 - The following data represent the time (in minutes)...Ch. 2 - The data below shows birth rate and per capita...Ch. 2 - The following is a USA Today-type graph. Do you...Ch. 2 - A bar graph or pie chart (or both) that depicts...Ch. 2 - A histogram that displays the distribution of...Ch. 2 - Six histograms displaying tornado duration for...Ch. 2 - A bar chart that shows the relationship between...Ch. 2 - A bar chart that shows the relationship between...Ch. 2 - A general summary of your findings and...
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