Solution Found!

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
Change Question

Three engineers are independently estimating the spring

Chapter 7, Problem 10E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Three engineers are independently estimating the spring constant of a spring, using the linear model specified by Hooke’s law. Engineer A measures the length of the spring under loads of 0, 1, 3, 4, and 6 lb, for a total of five measurements. Engineer B uses the same loads, but repeats the experiment twice, for a total of 10 independent measurements. Engineer C uses loads of 0, 2, 6, 8, and 12 lb, measuring once for each load. The engineers all use the same measurement apparatus and procedure. Each engineer computes a 95% confidence interval for the spring constant.

a. If the width of the interval of engineer A is divided by the width of the interval of engineer B, the quotient will be approximately__________ .

b. If the width of the interval of engineer A is divided by the width of the interval of engineer C, the quotient will be approximately__________ .

c. Each engineer computes a 95% confidence interval for the length of the spring under a load of 2.5 lb. Which interval is most likely to be the shortest? Which interval is most likely to be the longest?

Questions & Answers

QUESTION:

Three engineers are independently estimating the spring constant of a spring, using the linear model specified by Hooke’s law. Engineer A measures the length of the spring under loads of 0, 1, 3, 4, and 6 lb, for a total of five measurements. Engineer B uses the same loads, but repeats the experiment twice, for a total of 10 independent measurements. Engineer C uses loads of 0, 2, 6, 8, and 12 lb, measuring once for each load. The engineers all use the same measurement apparatus and procedure. Each engineer computes a 95% confidence interval for the spring constant.

a. If the width of the interval of engineer A is divided by the width of the interval of engineer B, the quotient will be approximately__________ .

b. If the width of the interval of engineer A is divided by the width of the interval of engineer C, the quotient will be approximately__________ .

c. Each engineer computes a 95% confidence interval for the length of the spring under a load of 2.5 lb. Which interval is most likely to be the shortest? Which interval is most likely to be the longest?

ANSWER:

Step 1 of 4

(a) Engineer A and Engineer B measure the length of the spring under the same loads.

The width of the confidence interval for the slope (spring constant) is twice the margin of error.

Since the two engineers use the same springs and loads, it is safe to assume that the standard deviation  is the same for the two engineers.

Add to cart

Study Tools You Might Need

Chapter: 15 Problem: 15.22

Classical Mechanics 0
A rocket is traveling at speed 0.9c along the x axis of frame 3. It shoots a bullet whose velocity v' (measured in the rocket's rest frame 3') is 0.9c along the y' axis of 3'. What is the bullet's velocity (magnitude and direction) as measured in 5?

Chapter: 22 Problem: 28E

Conceptual Physics 11
Problem 28E The proportionality constant k in Coulombs law is huge in ordinary units, whereas the proportionality constant G in Newtons law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

Chapter: 8 Problem: 2

Campbell Biology 9
Most cells cannot harness heat to perform work because a. heat is not a form of energy. b. cells do not have much heat; they are relatively cool. c. temperature is usually uniform throughout a cell. d. heat can never be used to do work. e. heat must remain constant during work

Chapter: 14 Problem: 3.1

Chemistry: The Central Science 12
The reaction between reactant \(A\) (blue spheres) and reactant \(B\) (red spheres) is shown in the following diagram: Based on this diagram, which equation best describes the reaction? [Section 3.1] (a) \(\mathrm{A}_{2}+\mathrm{B} \longrightarrow \mathrm{A}_{2} \mathrm{~B}\) (b) \(\mathr

Chapter: 9 Problem: 10

Principles of Economics 6
Consider a country that imports a good from abroad. For each of following statements, say whether it is true or false. Explain your answer. a. The greater the elasticity of demand, the greater the gains from trade. b. If demand is perfectly inelastic, there are no gains from trade. c. If demand is p

Chapter: 1 Problem: 23

Calculus: Early Transcendentals 9
Find a formula for the inverse of the function. \(f(x)=1-x^{2}, \quad x \geqslant 0\)

Chapter: 9 Problem: 13

Biology: Concepts and Applications 10
Where does translation take place in a eukaryotic cell?

Chapter: 8 Problem: 9

Behavior Modification: Principles and Procedures 6
What is a CER? Provide examples of positive and negative CERs.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back