Suppose we take the entire sample of ten normal(, 2 ) observations as a single sample.

Suppose we take the entire sample of ten normal(μ, σ²) observations as a single sample. We will start with the original prior we found in Exercise 15.3.
(a) Find the posterior using the macro NVarICP in Minitab or the function nvaricp in R.
(b) What do you notice from Exercises 15.3-15.5?
(c) Test the hypothesis H₀: σ ≤ 5 vs. H₁ : σ > 5 at the 5% level of significance.

Data From Exercise 15.3

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Suppose our prior belief is is just as likely to be below 8 as it is to be above 8. (Our prior distribution g() has median 8.) Determine an S an inverse chi-squared (K) that matches our prior median where we use K1 degree of freedom.