Hw 4

##8.3

"2p(x<k)-1=.8"

## [1] "2p(x<k)-1=.8"

"2p(x<k)=1.8"

## [1] "2p(x<k)=1.8"

"p(x<k)=.9"

## [1] "p(x<k)=.9"

qt(.9,6)

## [1] 1.439756

##8.4

1-pnorm(2)

## [1] 0.02275013

df <-c(40,20,10,5)
Pr<- 1-pt(2,df)

##8.5

t05 <- qt(.01, 9, lower.tail = FALSE)
# Take samples from a normal population with mean 5 and sd 8
mu <- 5
sigma <- 8
mean(replicate(10000, {
  X <- rnorm(20, mu, sigma) # sample of size 20
  Xbar <- 7 # sample mean
  SE <- sd(X) / sqrt(20) # standard error
  (Xbar - t05 * SE < mu) & (mu < Xbar + t05 * SE)
}))

## [1] 1

##8.7

t05 <- qt(.025, 99, lower.tail = FALSE)
Set<-morley
  mean = mean(morley$Speed)
 sd = sd(morley$Speed)
 SE <- sd / sqrt(100)
LB <- (mean - t05 * SE ) 

UB <- ( mean + t05 * SE)

LB

## [1] 836.7226

UB

## [1] 868.0774