Consider a data set about teacher workload in an area, the number of hours required to work at school (hrwork) per week were recorded. "hrwork.csv" contains the data set. A normal distribution N(,2) is assumed for these hrwork data. Conduct a Bayesian analysis for this data set to make inferences about the mean , and variance 2. Suppose the following conjugate prior is assigned:

2 inverse gamma(3, 36) |2 N(40,2/0.1)

dat2 = read.csv("teachers.csv", header = TRUE) y2 = dat2$hrwork

1. (1)(10 points) Draw independent samples from the posterior distribution.
2. (2)(5 points) Report 95% equal tails credible intervals for both and 2.
3. (3)(5 points) If another teacher is selected in this area and ask the same question, what is the probability that the number of hours required to work at school is greater than 38?