A5 Hypothesis Testing for the Population Mean

z-test for the Population Mean

load("time.RData")

hist(time$time1,xlab="Time Exercising Per Week", main="Sample 1")

hist(time$time2,xlab="Time Exercising Per Week", main="Sample 2")

hist(time$time3,xlab="Time Exercising Per Week", main="Sample 3")

hist(time$time4,xlab="Time Exercising Per Week", main="Sample 4")

n=5:15

z=(550-500)/(100/sqrt(n))

pvalue=1-pnorm(z)

significance=c(pvalue<0.05)

data.frame(n,z,pvalue,significance)

##     n        z     pvalue significance
## 1   5 1.118034 0.13177624        FALSE
## 2   6 1.224745 0.11033568        FALSE
## 3   7 1.322876 0.09293837        FALSE
## 4   8 1.414214 0.07864960        FALSE
## 5   9 1.500000 0.06680720        FALSE
## 6  10 1.581139 0.05692315        FALSE
## 7  11 1.658312 0.04862721         TRUE
## 8  12 1.732051 0.04163226         TRUE
## 9  13 1.802776 0.03571173         TRUE
## 10 14 1.870829 0.03068441         TRUE
## 11 15 1.936492 0.02640376         TRUE

load("Pregnancy.RData")

z.test = function(x, sig, mu0, alt="greater") {
  mu = mean(x);
  n = length(x);
  z = (mu-mu0)/(sig/sqrt(n));
  if (alt=="less"){p = pnorm(z)}
    else {
      if (alt=="two.sided"){p = 2*(1-pnorm(abs(z)))}
      else {p = 1-pnorm(z)}
    }
  paste("mean = ",mu,"n = ",n,", z = ",z,", p-value = ",round(p,5))
}

z.test(x=pregnancy$length, sig=16, mu0=266, alt="less")

## [1] "mean =  259.68 n =  25 , z =  -1.975 , p-value =  0.02413"

t-test for the Population Mean

load("drinks.RData")

t.test(drinks$drinks.per.week,mu = 4.73, alternative = "two.sided")

## 
##  One Sample t-test
## 
## data:  drinks$drinks.per.week
## t = -1.8275, df = 74, p-value = 0.07165
## alternative hypothesis: true mean is not equal to 4.73
## 95 percent confidence interval:
##  3.064735 4.801932
## sample estimates:
## mean of x 
##  3.933333