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###############################################
# Section 8.3 A One-Sided Test of a Normal Mean
###############################################
library(LearnBayes)
pmean=170; pvar=25
probH=pnorm(175,pmean,sqrt(pvar))
probA=1-probH
prior.odds=probH/probA
prior.odds
weights=c(182, 172, 173, 176, 176, 180, 173, 174, 179, 175)
xbar=mean(weights)
sigma2=3^2/length(weights)
post.precision=1/sigma2+1/pvar
post.var=1/post.precision
post.mean=(xbar/sigma2+pmean/pvar)/post.precision
c(post.mean,sqrt(post.var))
post.odds=pnorm(175,post.mean,sqrt(post.var))/
(1-pnorm(175,post.mean,sqrt(post.var)))
post.odds
BF = post.odds/prior.odds
BF
postH=probH*BF/(probH*BF+probA)
postH
z=sqrt(length(weights))*(mean(weights)-175)/3
1-pnorm(z)
weights=c(182, 172, 173, 176, 176, 180, 173, 174, 179, 175)
data=c(mean(weights),length(weights),3)
prior.par=c(170,1000)
mnormt.onesided(175,prior.par,data)
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