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Most sophomore physics students are required to conduct an
Chapter 11, Problem 26E(choose chapter or problem)
Most sophomore physics students are required to conduct an experiment verifying Hooke’s law. Hooke’s law states that when a force is applied to a body that is long in comparison to its cross-sectional area, the change y in its length is proportional to the force x; that is,
\(y=\beta_{1} x_{1}\)
where \(\beta_{1}\) is a constant of proportionality. The results of a physics student’s laboratory experiment are shown in the following table. Six lengths of steel wire, .34 millimeter (mm) in diameter and 2 meters (m) long, were used to obtain the six force-length change measurements.
a Fit the model, \(Y=\beta_{0}+\beta_{1} x+\varepsilon\), to the data, using the method of least squares.
b Find a 95% confidence interval for the slope of the line.
c According to Hooke’s law, the line should pass through the point (0, 0); that is, \(\beta_{0}\) should equal 0. Test the hypothesis that E(Y ) = 0 when x = 0. Give bounds for the attained significance level.
d Applet Exercise What is the exact p-value?
e What would you conclude at the \(\alpha=.05\) level?
Equation transcription:
Text transcription:
y=\beta{1} x{1}
beta_{1}
Y=beta{0}+beta{1} x+\varepsilon
beta_{0}
alpha=.05
Questions & Answers
QUESTION:
Most sophomore physics students are required to conduct an experiment verifying Hooke’s law. Hooke’s law states that when a force is applied to a body that is long in comparison to its cross-sectional area, the change y in its length is proportional to the force x; that is,
\(y=\beta_{1} x_{1}\)
where \(\beta_{1}\) is a constant of proportionality. The results of a physics student’s laboratory experiment are shown in the following table. Six lengths of steel wire, .34 millimeter (mm) in diameter and 2 meters (m) long, were used to obtain the six force-length change measurements.
a Fit the model, \(Y=\beta_{0}+\beta_{1} x+\varepsilon\), to the data, using the method of least squares.
b Find a 95% confidence interval for the slope of the line.
c According to Hooke’s law, the line should pass through the point (0, 0); that is, \(\beta_{0}\) should equal 0. Test the hypothesis that E(Y ) = 0 when x = 0. Give bounds for the attained significance level.
d Applet Exercise What is the exact p-value?
e What would you conclude at the \(\alpha=.05\) level?
Equation transcription:
Text transcription:
y=\beta{1} x{1}
beta_{1}
Y=beta{0}+beta{1} x+\varepsilon
beta_{0}
alpha=.05
ANSWER:Step 1 of 6
Given:
Data is given on the change in length measurements for different values of force applied to a steel wire.