Refer to the Meteoritics (Mar. 1995) study of lunar soil evolution, Exercise 8.62. Recall that one theory is that the proportion p of lunar soil grains that are coated with dust and/or glass fragments will be less than .5 at the bottom of the lunar core soil sample. Assuming that the prior distribution for p is a beta probability distribution with parameters α = 1 and β = 2, conduct a Bayesian test of the hypothesis of interest.

Data from Exercise 8.62

Meteoritics (March 1995) reported the results of a study of lunar soil evolution. Data were obtained from the Apollo 16 mission to the moon, during which a 62-cm core was extracted from the soil near the landing site. Monomineralic grains of lunar soil were separated out and examined for coating with dust and glass fragments. Each grain was then classified as coated or uncoated. Of interest is the “coat index,” that is, the proportion of grains that are coated. According to soil evolution theory, the coat index will exceed .5 at the top of the core, equal .5 in the middle of the core, and fall below .5 at the bottom of the core.

Transcribed Image Text:

Location (depth) тор (4.25 cm) Middle Bottom (28.1 cm) (54.5 cm) Number of Grains 84 73 81 Sampled Number Coated 64 35 29