Theory predicts that 8, the melting point of a particular substance under a pressure of 106 atmospheres, is 4.01. The procedure for measuring this melting point is fairly inaccurate, due to the high...

Theory predicts that 8, the melting point of a particular substance under a pressure of 106 atmospheres, is 4.01. The procedure for measuring this melting point is fairly inaccurate, due to the high pressure. Indeed it is known that an observation X has a .N( 8, 1) distribution. Five independent experiments give observations of 4.9, 5.6, 5.1,4.6, and 3.6. The prior probability that 8 = 4.01 is 0.5. The remaining values of 8 are given the density (0.5) gI(8), where gi is a .N(4.01, 1) density. Formulate and conduct a Bayesian test of the proposed theory.