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Chapter 7, Problem 2(choose chapter or problem)
Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) describes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. The following output (from MINITAB) describes the fit of a linear model that predicts the frequency (in ) in terms of the damping ratio for overdamped (damping ratio
modes. There are \(n=7\) observations.
The regression equation is |
||||
Frequency |
Coef |
T |
P |
|
Predictor |
||||
Constant |
||||
Damping Ratio |
a. How many degrees of freedom are there for the Student's statistics?
b. Find a confidence interval for \(\beta_1\).
c. Find a confidence interval for \(\beta_0\).
d. Someone claims that the frequency decreases by if the damping ratio increases by
Use the given output to perform a hypothesis test to determine whether this claim is plausible.
Equation Transcription:
Text Transcription:
n=7
beta_1
beta_0
Questions & Answers
QUESTION:
Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) describes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. The following output (from MINITAB) describes the fit of a linear model that predicts the frequency (in ) in terms of the damping ratio for overdamped (damping ratio
modes. There are \(n=7\) observations.
The regression equation is |
||||
Frequency |
Coef |
T |
P |
|
Predictor |
||||
Constant |
||||
Damping Ratio |
a. How many degrees of freedom are there for the Student's statistics?
b. Find a confidence interval for \(\beta_1\).
c. Find a confidence interval for \(\beta_0\).
d. Someone claims that the frequency decreases by if the damping ratio increases by
Use the given output to perform a hypothesis test to determine whether this claim is plausible.
Equation Transcription:
Text Transcription:
n=7
beta_1
beta_0
ANSWER:
Step 1 of 4
a)
Given:
(a) The degrees of freedom is the sample size 
