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 Hz) in terms of the damping ratio for overdamped (damping ratio > 1) modes. There are n = 7 observations.

a. How many degrees of freedom are there for the Student??s t statistics?

b. Find a 98% confidence interval for β1.

c. Find a 98% confidence interval for β0.

d. Someone claims that the frequency decreases by 0.6 Hz if the damping ratio increases by 1. Use the given output to perform a hypothesis test to determine whether this claim is plausible.

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The regression equation is Frequency = 0.773 - 0.280 Damping Ratio Predictor Coef SE Coef P Constant 0.77289 0.14534 5.3176 0.003 Damping Ratio -0.27985 0.079258 -3.5309 0.017