# Example 1.1
# ==================
#  X ~ N(10, 1.5^2)

# (1) Find P(8 < X <12)
pnorm(12, mean=10, sd=1.5) - pnorm(8, mean=10, sd=1.5)
# 0.8176

# (2) Find P(X > 13 | X >6)
(1-pnorm(13, 10, 1.5))/(1-pnorm(6, 10, 1.5))
# 0.0228




# Example 1.2
# =================

x <- scan()
80 80 79 81 76 66 71 76 70 85

x.bar <- mean(x)
s2 <- var(x)
sd <- sqrt(var(x))
qt(.95, 9) # 1.833113
qt(.975, 9) # 2.262157

# 95% Confidence Interval
result1 <- t.test(x, alternative="two.sided", conf.level=0.95)
names(result1); result1$conf.int
# 72.22606 80.57394  

# One-Sided t Test
result2 <- t.test(x, alternative="greater", mu=75, conf.level=0.95); result2
cbind(t= result2$statistic, df=result2$parameter, p.value=result2$p.value)




--------------------------------------------------------------
        One Sample t-test

data:  x 
t = 0.7588, df = 9, p-value = 0.2337
alternative hypothesis: true mean is greater than 75 
95 percent confidence interval:
 73.0177     Inf 
sample estimates:
mean of x 
     76.4 
     
          
    t       df  p.value
t 0.7587608  9 0.2337003
-----------------------------------------------------------------