A4 Probability

Probability: Random Variables

pnorm(700, mean=507, sd=111)

## [1] 0.9589596

1 - pnorm(700, mean=507, sd=111)

## [1] 0.04104036

pnorm(65, mean=69, sd=2.8)

## [1] 0.07656373

1 - pnorm(75, mean=69, sd=2.8)

## [1] 0.01606229

pnorm(72, mean=69, sd=2.8) - pnorm(66, mean=69, sd=2.8)

## [1] 0.7160232

qnorm(0.98, mean=507, sd=111)

## [1] 734.9661

qnorm(0.005, mean=69, sd=2.8)

## [1] 61.78768

qnorm((1-0.0025), mean=69, sd=2.8)

## [1] 76.85969

Inference: Estimation

load("birthweight.RData")

x=birthweight$birthweight

C=0.99
z=qnorm((1+C)/2)

stdev=500

n=length(x)
xbar=mean(x)

xbar-z*(stdev/sqrt(n))

## [1] 2996.165

xbar+z*(stdev/sqrt(n))

## [1] 3226.555

load("sleep.RData")

t.test(sleep$sleep, conf.level=0.95)$conf.int

## [1] 7.090439 7.620828
## attr(,"conf.level")
## [1] 0.95

load("guns.RData")

n=length(support$opinion);n

## [1] 1200

t=table(support$opinion);t

## 
## not satisfied     satisfied 
##          1058           142

t[1]

## not satisfied 
##          1058

t[2]

## satisfied 
##       142

prop.test(t[1],n,conf.level=0.95)

## 
##  1-sample proportions test with continuity correction
## 
## data:  t[1] out of n, null probability 0.5
## X-squared = 697.69, df = 1, p-value < 2.2e-16
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.8617191 0.8991231
## sample estimates:
##         p 
## 0.8816667

prop.test(t[2],n,conf.level=0.95)$conf.int

## [1] 0.1008769 0.1382809
## attr(,"conf.level")
## [1] 0.95