We are interested in determining the dielectric constant,Eof a new material our lab has developed. The new material was derived using a variation of existing methods, and you know the material should have a value of e~ 2.50. There was only a limited eoretically, amount of time for experiments and the following data was obtained after conducting only n-4 repetitions {2.749, 2.866, 2.420, 1.637) a) Letting Y be the random variable corresponding to the experimental value of the dielectric constant, report an estimate of y and a 95% CI using standard statistical methods. Show all your work. b) Now we will try a Bayesian approach. Use as previous knowledge, your theoretical value ofe along with a weighting factor of Ko-10 to determine a Bayesian estimate of μy. Provide a 95% Bayesian coverage interval. A good set of starting parameters for the variance are Vo-1 and ơ2-0.25. Show all your work and provide hardcopies of all code used. c) The true value for uy is 2.55. Comment on why the Bayesian method provided much better results compared to traditional methods.
