ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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Chapter 2, Problem 29CQ
To determine
To identify: The thing which misleading the given graph.
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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 2 Solutions
ALEKS 360 ELEM STATISTICS
Ch. 2.1 - Ages of Presidents at Inauguration The data...Ch. 2.1 - List five reasons for organizing data into a...Ch. 2.1 - Name the three types of frequency distributions,...Ch. 2.1 - How many classes should frequency distributions...Ch. 2.1 - What are open-ended frequency distributions? Why...Ch. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - For Exercises 58, find the class boundaries,...Ch. 2.1 - For Exercises 912, show frequency distributions...
Ch. 2.1 - For Exercises 912, show frequency distributions...Ch. 2.1 - For Exercises 912, show frequency distributions...Ch. 2.1 - For Exercises 912, show frequency distributions...Ch. 2.1 - Favorite Coffee Flavor A survey was taken asking...Ch. 2.1 - Trust in Internet Information A survey was taken...Ch. 2.1 - Eating at Fast Food Restaurants A survey was taken...Ch. 2.1 - Ages of Dogs The ages of 20 dogs in a pet shelter...Ch. 2.1 - Maximum Wind Speeds The data show the maximum wind...Ch. 2.1 - Stories in the Worlds Tallest Buildings The number...Ch. 2.1 - Ages of Declaration of Independence Signers The...Ch. 2.1 - Salaries of Governors Here are the salaries (in...Ch. 2.1 - Charity Donations A random sample of 30 large...Ch. 2.1 - Unclaimed Expired Prizes The number of unclaimed...Ch. 2.1 - Scores in the Rose Bowl The data show the scores...Ch. 2.1 - Consumption of Natural Gas Construct a frequency...Ch. 2.1 - Average Wind Speeds A sample of 40 large cities...Ch. 2.1 - Percentage of People Who Completed 4 or More Years...Ch. 2.1 - JFK Assassination A researcher conducted a survey...Ch. 2.1 - The Value of Pi The ratio of the circumference of...Ch. 2.2 - Selling Real Estate Assume you are a realtor in...Ch. 2.2 - Do Students Need Summer Development? For 108...Ch. 2.2 - Bear Kills The number of bears killed in 2014 for...Ch. 2.2 - Pupils Per Teacher The average number of pupils...Ch. 2.2 - Number of College Faculty The number of faculty...Ch. 2.2 - Railroad Crossing Accidents The data show the...Ch. 2.2 - NFL Salaries The salaries (in millions of dollars)...Ch. 2.2 - Suspension Bridges Spans The following frequency...Ch. 2.2 - Costs of Utilities The frequency distribution...Ch. 2.2 - Air Pollution One of the air pollutants that is...Ch. 2.2 - Making the Grade The frequency distributions shown...Ch. 2.2 - Blood Glucose Levels The frequency distribution...Ch. 2.2 - Waiting Times The frequency distribution shows the...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Construct a histogram, frequency polygon, and...Ch. 2.2 - Home Runs The data show the most number of home...Ch. 2.2 - Protein Grams in Fast Food The amount of protein...Ch. 2.2 - Using the histogram shown here, do the following....Ch. 2.2 - Using the results from Exercise 19. answer these...Ch. 2.2 - Math SAT Scores Shown is an ogive depicting the...Ch. 2.3 - Applying the Concepts 23 Causes of Accidental...Ch. 2.3 - Tech Company Employees Construct a vertical and...Ch. 2.3 - Worldwide Sales of Fast Foods The worldwide sales...Ch. 2.3 - Gulf Coastlines Construct a Pareto chart for the...Ch. 2.3 - Roller Coaster Mania The World Roller Coaster...Ch. 2.3 - Online Ad Spending The amount spent (in billions...Ch. 2.3 - Violent Crimes The number of all violent crimes...Ch. 2.3 - U.S. Licensed Drivers 70 or Older Draw a time...Ch. 2.3 - Valentines Day Spending The data show the average...Ch. 2.3 - Credit Cards Draw and analyze a pie graph for the...Ch. 2.3 - Reasons We Travel The following data are based on...Ch. 2.3 - Kids and Guns The following data show where...Ch. 2.3 - Colors of Automobiles The popular car colors are...Ch. 2.3 - Ages of Football Players The data show the ages of...Ch. 2.3 - Teacher Strikes In Pennsylvania the numbers of...Ch. 2.3 - Years of Experience The data show the number of...Ch. 2.3 - Commuting Times Fifty off-campus students were...Ch. 2.3 - Home Run Club There are 43 Major League baseball...Ch. 2.3 - Calories in Salad Dressings A listing of calories...Ch. 2.3 - Length of Major Rivers The data show the lengths...Ch. 2.3 - Math and Reading Achievement Scores The math and...Ch. 2.3 - State which type of graph (Pareto chart, time...Ch. 2.3 - State which graph (Pareto chart, time series...Ch. 2.3 - U.S. Health Dollar The U.S. health dollar is spent...Ch. 2.3 - Prob. 24ECh. 2.3 - Cost of Milk The graph shows the increase in the...Ch. 2.3 - U.S. Population by Age The following information...Ch. 2.3 - Chicago Homicides Draw and compare two time series...Ch. 2.3 - Trip Reimbursements The average amount requested...Ch. 2 - How People Get Their News The Brunswick Research...Ch. 2 - Mens World Hockey Champions The United States won...Ch. 2 - BUN Count The blood urea nitrogen (BUN) count of...Ch. 2 - Wind Speed The data show the average wind speed...Ch. 2 - Waterfall Heights The data show the heights (in...Ch. 2 - Ages of the Vice Presidents at the Time of Their...Ch. 2 - Find the relative frequency for the frequency...Ch. 2 - Find the relative frequency for the frequency...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Non-Alcoholic Beverages The data show the yearly...Ch. 2 - Calories of Nuts The data show the number of...Ch. 2 - Crime The data show the percentage of the types of...Ch. 2 - AID: 1825 | 31/5/2018 16. Pet Care The data (in...Ch. 2 - Broadway Stage Engagements The data show the...Ch. 2 - High School Dropout Rate The data show the high...Ch. 2 - Prob. 2.3.19RECh. 2 - Smart Phone Insurance Construct and analyze a pie...Ch. 2 - Prob. 2.3.21RECh. 2 - Prob. 2.3.22RECh. 2 - Weights of Football Players A local football team...Ch. 2 - Public Libraries The numbers of public libraries...Ch. 2 - Pain Relief The graph below shows the time it...Ch. 2 - Casino Payoffs The graph shows the payoffs...Ch. 2 - From the Data Bank located in Appendix B, choose...Ch. 2 - Prob. 2DACh. 2 - From the Data Bank, select at least 30 subjects...Ch. 2 - Prob. 4DACh. 2 - Using the data from Data Set XI in Appendix B,...Ch. 2 - Prob. 7DACh. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 2CQCh. 2 - Prob. 3CQCh. 2 - Frequency distributions can aid the researcher in...Ch. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 6CQCh. 2 - Determine whether each statement is true or false....Ch. 2 - Prob. 8CQCh. 2 - What are the boundaries for 8.68.8? a. 89 b....Ch. 2 - What graph should be used to show the relationship...Ch. 2 - Prob. 11CQCh. 2 - The three types of frequency distributions are...Ch. 2 - In a frequency distribution, the number of classes...Ch. 2 - Prob. 14CQCh. 2 - Data collected over a period of time can be...Ch. 2 - A statistical device used in exploratory data...Ch. 2 - On a Pareto chart, the frequencies should be...Ch. 2 - Housing Arrangements A questionnaire on housing...Ch. 2 - Housing Arrangements A questionnaire on housing...Ch. 2 - Prob. 20CQCh. 2 - Construct a histogram, a frequency polygon, and an...Ch. 2 - Coal Consumption The following data represent the...Ch. 2 - Construct a histogram, frequency polygon, and...Ch. 2 - Recycled Trash Construct a Pareto chart and a...Ch. 2 - Identity Thefts The results of a survey of 84...Ch. 2 - Needless Deaths of Children The New England...Ch. 2 - Prob. 27CQCh. 2 - Parking Meter Revenue In a small city the number...Ch. 2 - Prob. 29CQCh. 2 - The Great Lakes Shown are various statistics about...Ch. 2 - Teacher Strikes In Pennsylvania there were more...
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