Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 45SE
Car Insurance and Age The following graph shows the average car insurance premium for a sample of ages. (Source: valuepenguin.com)
a. Explain what the graph tells us about insurance rates for drivers at different ages. Explain why insurance rates might follow this trend.
b. Would it be appropriate to do a linear
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Business
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 4 Solutions
Introductory Statistics
Ch. 4 - GPA Predictors The scatterplots show SAT scores...Ch. 4 - Salary and Employment The first graph shows the...Ch. 4 - Age and Credits The scatterplot below shows data...Ch. 4 - Age and GPA The scatterplot shows data on age and...Ch. 4 - Credits and GPA (Example 1) The scatterplot shows...Ch. 4 - Salary and Education The scatterplot shows data on...Ch. 4 - Sisters and Brothers The scatterplot shows the...Ch. 4 - House Price and Area Describe the trend in the...Ch. 4 - Work and TV The scatterplot shows the number of...Ch. 4 - Work and Sleep The scatterplot shows the number of...
Ch. 4 - Age and Sleep The scatterplot shows the age and...Ch. 4 - Height and Weight for Women The figure shows a...Ch. 4 - College Tuition and ACT a. The first scatterplot...Ch. 4 - Ages of Women Who Give Birth The figure shows a...Ch. 4 - Law School The scatterplot shows the LSAT (Law...Ch. 4 - Medical School The scatterplot shows the...Ch. 4 - Matching Pick the letter of the graph that goes...Ch. 4 - Matching Pick the letter of the graph that goes...Ch. 4 - Matching Match each of the following correlations...Ch. 4 - Matching Match each of the following correlations...Ch. 4 - Airline Tickets (Example 2) The distance (in...Ch. 4 - Train Tickets The table for part (a) shows...Ch. 4 - SAT and GPA In Exercise 4.1 there is a graph of...Ch. 4 - House Price The correlation between house price...Ch. 4 - Rate My Professor Seth Wagerman, a former...Ch. 4 - Cousins Five people were asked how many female...Ch. 4 - GPA and Gym Use USA Today College published an...Ch. 4 - Education and Life Expectancy United Press...Ch. 4 - Salaries of College Graduates (Example 3) The...Ch. 4 - Mother and Daughter Heights The graph shows the...Ch. 4 - Median Weekly Earning by Gender The scatterplot...Ch. 4 - Home Prices and Size The scatterplot shows the...Ch. 4 - Height and Arm Span for Women (Example 4) TI-84...Ch. 4 - Hand and Foot Length for Women The computer output...Ch. 4 - Height and Arm Span for Men (Example 5)...Ch. 4 - Hand Length and Foot Length for Men Measurements...Ch. 4 - Comparing Correlation for Arm Span and Height The...Ch. 4 - Age and Weight for Men and Women The scatterplot...Ch. 4 - Singles and Doubles Winning Percentage The...Ch. 4 - Seesaw The figure shows a scatterplot of the...Ch. 4 - Choosing the Predictor and Response Variables...Ch. 4 - Choosing the Predictor and the Response Variable...Ch. 4 - Percentage of Smoke-Free Homes and Percentage of...Ch. 4 - Effect of Adult Smoking on High School Student...Ch. 4 - Car Insurance and Age The following graph shows...Ch. 4 - Life Insurance and Age The graph shows the monthly...Ch. 4 - How Is the Time of a Flight Related to the...Ch. 4 - Distance and Train Ticket Price The following...Ch. 4 - Do States with Higher Populations Have More...Ch. 4 - Movie Ratings The following table give the Rotten...Ch. 4 - Pitchers The table shows the Earned Run Average...Ch. 4 - Text Messages The following table shows the number...Ch. 4 - Answer the questions using complete sentences. a....Ch. 4 - Answer the questions using complete sentences. a....Ch. 4 - If there is a positive correlation between number...Ch. 4 - Suppose that the growth rate of children looks...Ch. 4 - Coefficient of Determination If the correlation...Ch. 4 - Coefficient of Determination Does a correlation of...Ch. 4 - Investing Some investors use a technique called...Ch. 4 - Blood Pressure Suppose a doctor telephones those...Ch. 4 - Salary and Year of Employment (Example 8) The...Ch. 4 - MPG: Highway and City The following figure shows...Ch. 4 - Cost of Turkeys The following table shows the...Ch. 4 - Wine Calories The table shows the calories in a...Ch. 4 - Teacher Pay and Expenditure Per Student (Example...Ch. 4 - Teacher Pay and High School Graduation Rates The...Ch. 4 - Does Having a Job Affect Students’ Grades?...Ch. 4 - Weight of Trash and Household Size Data were...Ch. 4 - Predicting Home Runs Data on the number of home...Ch. 4 - Predicting 3-Point Baskets Data on the 3-point...Ch. 4 - 4th-Grade Reading and Math Scores Data from the...Ch. 4 - SAT Scores The following table shows the average...Ch. 4 - Test Scores Assume that in a political science...Ch. 4 - Test Scores Assume that in a sociology class, the...Ch. 4 - Heights and Weights of People The following table...Ch. 4 - Heights and Weights of Men The table shows the...Ch. 4 - Prob. 77CRECh. 4 - Granola Bars The following table shows the fat...Ch. 4 - Shoe Size and Height The scatterplot shows the...Ch. 4 - Age and Sleep The following scatterplot shows the...Ch. 4 - Age and Weight The following scatterplot shows the...Ch. 4 - Heights and Test Scores a. The following figure...Ch. 4 - Law School Selectivity and Employment The...Ch. 4 - Prob. 84CRECh. 4 - Prob. 87CRECh. 4 - Fuel-Efficient Cars The following table gives the...Ch. 4 - Tall Buildings The following scatterplot shows...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - The following figure shows a scatterplot of the...Ch. 4 - Wages and Education The figure shows a scatterplot...Ch. 4 - Do Students Taking More Units Study More Hours?...Ch. 4 - Hours of Exercise and Hours of Homework The...Ch. 4 - Children’s Ages and Heights The following figure...Ch. 4 - Blackjack Tips The following figure shows the...Ch. 4 - Decrease in Cholesterol A doctor is studying...Ch. 4 - Prob. 102CRE
Additional Math Textbook Solutions
Find more solutions based on key concepts
Fill in each blank so that the resulting statement is true.
1. The degree of the polynomial function is _____....
Algebra and Trigonometry (6th Edition)
The largest polynomial that divides evenly into a list of polynomials is called the _______.
Elementary & Intermediate Algebra
Is there a relationship between wine consumption and deaths from heart disease? The table gives data from 19 de...
College Algebra Essentials (5th Edition)
Find all solutions of each equation in the interval .
Precalculus: A Unit Circle Approach (3rd Edition)
Let F be a continuous distribution function. If U is uniformly distributed on (0,1), find the distribution func...
A First Course in Probability (10th Edition)
Students in a Listening Responses class bought 40 tickets for a piano concert. The number of tickets purchased ...
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 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.arrow_forward2. Hypothesis Testing - Two Sample Means A nutritionist is investigating the effect of two different diet programs, A and B, on weight loss. Two independent samples of adults were randomly assigned to each diet for 12 weeks. The weight losses (in kg) are normally distributed. Sample A: n = 35, 4.8, s = 1.2 Sample B: n=40, 4.3, 8 = 1.0 Questions: a) State the null and alternative hypotheses to test whether there is a significant difference in mean weight loss between the two diet programs. b) Perform a hypothesis test at the 5% significance level and interpret the result. c) Compute a 95% confidence interval for the difference in means and interpret it. d) Discuss assumptions of this test and explain how violations of these assumptions could impact the results.arrow_forward1. Sampling Distribution and the Central Limit Theorem A company produces batteries with a mean lifetime of 300 hours and a standard deviation of 50 hours. The lifetimes are not normally distributed—they are right-skewed due to some batteries lasting unusually long. Suppose a quality control analyst selects a random sample of 64 batteries from a large production batch. Questions: a) Explain whether the distribution of sample means will be approximately normal. Justify your answer using the Central Limit Theorem. b) Compute the mean and standard deviation of the sampling distribution of the sample mean. c) What is the probability that the sample mean lifetime of the 64 batteries exceeds 310 hours? d) Discuss how the sample size affects the shape and variability of the sampling distribution.arrow_forward
- A biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?arrow_forwardBusinessarrow_forwardWhat is the solution and answer to question?arrow_forward
- To: [Boss's Name] From: Nathaniel D Sain Date: 4/5/2025 Subject: Decision Analysis for Business Scenario Introduction to the Business Scenario Our delivery services business has been experiencing steady growth, leading to an increased demand for faster and more efficient deliveries. To meet this demand, we must decide on the best strategy to expand our fleet. The three possible alternatives under consideration are purchasing new delivery vehicles, leasing vehicles, or partnering with third-party drivers. The decision must account for various external factors, including fuel price fluctuations, demand stability, and competition growth, which we categorize as the states of nature. Each alternative presents unique advantages and challenges, and our goal is to select the most viable option using a structured decision-making approach. Alternatives and States of Nature The three alternatives for fleet expansion were chosen based on their cost implications, operational efficiency, and…arrow_forwardBusinessarrow_forwardWhy researchers are interested in describing measures of the center and measures of variation of a data set?arrow_forward
- WHAT IS THE SOLUTION?arrow_forwardThe following ordered data list shows the data speeds for cell phones used by a telephone company at an airport: A. Calculate the Measures of Central Tendency from the ungrouped data list. B. Group the data in an appropriate frequency table. C. Calculate the Measures of Central Tendency using the table in point B. 0.8 1.4 1.8 1.9 3.2 3.6 4.5 4.5 4.6 6.2 6.5 7.7 7.9 9.9 10.2 10.3 10.9 11.1 11.1 11.6 11.8 12.0 13.1 13.5 13.7 14.1 14.2 14.7 15.0 15.1 15.5 15.8 16.0 17.5 18.2 20.2 21.1 21.5 22.2 22.4 23.1 24.5 25.7 28.5 34.6 38.5 43.0 55.6 71.3 77.8arrow_forwardII Consider the following data matrix X: X1 X2 0.5 0.4 0.2 0.5 0.5 0.5 10.3 10 10.1 10.4 10.1 10.5 What will the resulting clusters be when using the k-Means method with k = 2. In your own words, explain why this result is indeed expected, i.e. why this clustering minimises the ESS map.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY