The study on acid concentration in cheese included a total of 30 lactic acid measurements, the 10 given in Example 8.5.4 on page 487 and the following additional 20:
1.68, 1.9, 1.06, 1.3, 1.52, 1.74, 1.16, 1.49, 1.63, 1.99,
1.15, 1.33, 1.44, 2.01, 1.31, 1.46, 1.72, 1.25, 1.08, 1.25.
a. Using the same prior as in Example 8.6.2 on page 498, compute the posterior distribution of μ and τ based on all 30 observations.
b. Use the posterior distribution found in Example 8.6.2 on page 498 as if it were the prior distribution before observing the 20 observations listed in this problem. Use these 20 new observations to find the posterior distribution of μ and τ and compare the result to the answer to part (a).