Answer Happy

7. A biologist is studying puffin chicks west of mainland Orkney. Assume the wing length of chicks (in mm) is normally distributed with known standard deviation 15. Prior to observing data, the biologist believes the distribution of wing lengths to be normal with mean 100mm and standard deviation 12mm. A random sample of 20 chicks west of mainland Orkney reveals a mean wing length of 120mm. The wing lengths are thought to still be normally distributed. (a) Obtain a 95% credible interval for the mean value of the wing lengths of these chicks. [4 Marks] Hint: with prior distribution ~N(o,) and X₁,...,X, iids with N(μ, ²), the posterior distribution of u is N(A₁, 87) with 1 A₁ = and 4+ •+/ a (b) Using the data above, use a Bayesian hypothesis test to test the hypothesis Ho μ≤100 against the alternative Ha: > 100. [3 marks] +40