A class of 63 students has two hourly exams and a final exam. The regression model was constructed to predict the poerfomance on the final exam based on the results of the two hour exams
(x, and x2). The following are some quantities of interest:
0.9129168 -0.00981502 -0.00071092
(x'x)-' -0.00981502 1.497241e-04 -4.15806 - 05
(-0.00071092 -4.158056 - 05 5.81235e - 05
4871.0
(X'y) = 426011.0
367576.5
Assume y'y = {y} = 411, 222.7041.
63
(a) Find a 95% confidence interval for the coefficient of hourly 1 test.
Round your answers to three decimal places (e. g. 98.765).
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(b) Find a 95% confidence interval for the mean final grade for students who score 80 on the first test and 85 on the second.
Round your answers to two decimal places (e. g. 98.76).
IS Hylxo
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Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?