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In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from time t = 0.1 to t = 1.0. The data are presented in the following table. 0.1 0.03 0.2 0.1 0.3 0.27 0.4 0.47 0.5 0.73 0.6 1.07 0.7 1.46 0.8 1.89 0.9 2.39 1.0 2.95 The data follow the quadratic model y = h + B,t + ß;f +€, where Bo represents the initial position of the object, B, represents the initial velocity of the object, and B2 = a/2, where a is the acceleration of the object, assumed to be constant. In a perfect experiment, both the position and velocity of the object would be zero at time 0. However, due to experimental error, it is possible that the position and velocity at t = 0 are nonzero. Fit the quadratic model y = , + B,t+ b;² +e. a. b. Find a 95% confidence interval for B2. C. Find a 95% confidence interval for the acceleration a. d. Compute the P-value for each coefficient. e. Can you conclude that the initial position was not zero? Explain. f. Can you conclude that the initial velocity was not zero? Explain.

In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from time t = 0.1 to t = 1.0. The data are presented in the following table. 0.1 0.03 0.2 0.1 0.3 0.27 0.4 0.47 0.5 0.73 0.6 1.07 0.7 1.46 0.8 1.89 0.9 2.39 1.0 2.95 The data follow the quadratic model y = h + B,t + ß;f +€, where Bo represents the initial position of the object, B, represents the initial velocity of the object, and B2 = a/2, where a is the acceleration of the object, assumed to be constant. In a perfect experiment, both the position and velocity of the object would be zero at time 0. However, due to experimental error, it is possible that the position and velocity at t = 0 are nonzero. Fit the quadratic model y = , + B,t+ b;² +e. a. b. Find a 95% confidence interval for B2. C. Find a 95% confidence interval for the acceleration a. d. Compute the P-value for each coefficient. e. Can you conclude that the initial position was not zero? Explain. f. Can you conclude that the initial velocity was not zero? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from time t = 0.1 to t = 1.0. The data are presented in the following table. 0.1 0.03 0.2 0.1 0.3 0.27 0.4 0.47 0.5 0.73 0.6 1.07 0.7 1.46 0.8 1.89 0.9 2.39 1.0 2.95 The data follow the quadratic model y = h + B,t + ß;f +€, where Bo represents the initial position of the object, B, represents the initial velocity of the object, and B2 = a/2, where a is the acceleration of the object, assumed to be constant. In a perfect experiment, both the position and velocity of the object would be zero at time 0. However, due to experimental error, it is possible that the position and velocity at t = 0 are nonzero. Fit the quadratic model y = , + B,t+ b;² +e. a. b. Find a 95% confidence interval for B2. C. Find a 95% confidence interval for the acceleration a. d. Compute the P-value for each coefficient. e. Can you conclude that the initial position was not zero? Explain. f. Can you conclude that the initial velocity was not zero? Explain.
Transcribed Image Text:In an experiment to estimate the acceleration of an object down an inclined plane, the object is released and its distance in meters (y) from the top of the plane is measured every 0.1 second from time t = 0.1 to t = 1.0. The data are presented in the following table. 0.1 0.03 0.2 0.1 0.3 0.27 0.4 0.47 0.5 0.73 0.6 1.07 0.7 1.46 0.8 1.89 0.9 2.39 1.0 2.95 The data follow the quadratic model y = h + B,t + ß;f +€, where Bo represents the initial position of the object, B, represents the initial velocity of the object, and B2 = a/2, where a is the acceleration of the object, assumed to be constant. In a perfect experiment, both the position and velocity of the object would be zero at time 0. However, due to experimental error, it is possible that the position and velocity at t = 0 are nonzero. Fit the quadratic model y = , + B,t+ b;² +e. a. b. Find a 95% confidence interval for B2. C. Find a 95% confidence interval for the acceleration a. d. Compute the P-value for each coefficient. e. Can you conclude that the initial position was not zero? Explain. f. Can you conclude that the initial velocity was not zero? Explain.
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