Skip to main content

Math Statistics An Introduction to Statistical Methods and Data Analysis

A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data are presented here. a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses? b. Estimate the standard deviation in the speeds of the vehicles traveling on the interstate using a 95% confidence interval. c. Do the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use α = .05 in reaching your conclusion. d. To what population can the inferences obtained in parts (b) and (c) be validly applied?

A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data are presented here. a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses? b. Estimate the standard deviation in the speeds of the vehicles traveling on the interstate using a 95% confidence interval. c. Do the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use α = .05 in reaching your conclusion. d. To what population can the inferences obtained in parts (b) and (c) be validly applied?

Solution Summary: The author explains that the data indicates that there are violations of the necessary conditions to generate confidence interval and hypotheses testing to use the chi-square procedures.

An Introduction to Statistical Methods and Data Analysis

An Introduction to Statistical Methods and Data Analysis

7th Edition

ISBN: 9781305269477

Author: R. Lyman Ott, Micheal T. Longnecker

Publisher: Cengage Learning

See similar textbooks

Videos

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 7.7, Problem 5E

Chapter 7.7, Problem 7E

Chapter 7 Solutions

An Introduction to Statistical Methods and Data Analysis

Ch. 7.7 - A leading researcher in the study of interstate...Ch. 7.7 - Baseballs vary somewhat in their rebounding...Ch. 7.7 - Random samples of sizes n1 = 25 and n2 = 20 were...Ch. 7.7 - A soft-drink firm is evaluating an investment in a...Ch. 7.7 - A wildlife biologist was interested in determining...Ch. 7.7 - Prob. 30SE

Knowledge Booster

Background pattern image

$Statistics$

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.

Recommended textbooks for you

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt

Text book image

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

Text book image

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Text book image

Big Ideas Math A Bridge To Success Algebra 1: Stu...

Algebra

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:Houghton Mifflin Harcourt

SEE MORE TEXTBOOKS

What Are Research Ethics?; Author: HighSchoolScience101;https://www.youtube.com/watch?v=nX4c3V23DZI;License: Standard YouTube License, CC-BY

What is Ethics in Research - ethics in research (research ethics); Author: Chee-Onn Leong;https://www.youtube.com/watch?v=W8Vk0sXtMGU;License: Standard YouTube License, CC-BY