5-43. An article in the Journal of Aircraft (Vol. 23, 1986, pp. 859-864) describes a new equivalent plate analysis method. formulation that is capable of modeling aircraft structures such as cranked wing boxes and that produces results similar to the more computationally intensive finite element analysis method. Natural vibration frequencies for the cranked wing box struc- ture are calculated using both methods, and results for the first seven natural frequencies are shown here. Finite Element, Plate, Car Cycle/s Cycle/s Car Car 14.76 5 49.10 99.99 7 117.53 1 2 3 4 14.58 48.52 Equivalent 97.22 113.99 Finite Element, Cycle/s Cycle/s 174.73 6 212.72 277.38 Equivalent Plate, Cycle/s 181.22 220.14 294.80 (a) Do the data suggest that the two methods provide the same mean value for natural vibration frequency? Use the P-value approach.

Perform the exercise manually. Please

Q-(2)

The article "Polyhedral Distortions in Tourmaline" (A. Eril, J. Hughes, et al., The Canadian Mineralogist, 2002 153-162) presents a model for calculating bond-length distortion in vanadium-bearing tourmaline. To check the accuracy of the model, several calculated values (x) were compared with directly observed values (y) The results (read from a graph) are presented in the following table. Observed Value Calculated Value 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value…