R/OneSampleCI.R

In Harrindy/StatEngine: An R Package for the UofSC Course STAT 509 "Statistics for Engineers"

t.quantile=function(df,q)
{
  if(df<=0){return("df must be positive")}
  if(q<=0|q>=1){return("q must be between 0 and 1")}
  return(qt(q,df))
}


Chi2.quantile=function(df,q)
{
  if(df<=0){return("df must be positive")}
  if(q<=0|q>=1){return("q must be between 0 and 1")}
  return(qchisq(q,df))
}



Zinterval=function(level=0.95,sigma,sample,n,barx)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(sigma)==TRUE){
    return("Please provide the value of sigma.
           If it is unknown, consider Tinterval")
  }
  if(missing(sample)==FALSE){
    n=length(sample)
    barx=mean(sample)
  }else if(missing(n)==TRUE | missing(barx)==TRUE)
  {
    return("No sample was provided, please input the sample size/sample mean")
  }
  alpha=1-level
  z_a=qnorm(1-alpha/2)
  cat("The sample mean is", barx,"and sample size is", n,"\n")
  cat("A", level*100, "% two-sided confidence interval for the population mean is [", barx-z_a*sigma/sqrt(n),",",barx+z_a*sigma/sqrt(n),"]","\n")
  z_a=qnorm(1-alpha)
  cat("A", level*100, "% upper-confidence bound for the population mean is", barx+z_a*sigma/sqrt(n),"\n")
  cat("A", level*100, "% lower-confidence bound for the population mean is", barx-z_a*sigma/sqrt(n),"\n")
}

AZinterval=function(level=0.95,sample,n,barx,s)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(sample)==FALSE){
    n=length(sample)
    barx=mean(sample)
    s=sd(sample)
  }else if(missing(n)==TRUE | missing(barx)==TRUE | missing(s)==TRUE)
  {
    return("No sample was provided, please input the sample size/sample mean/sample standard deviation")
  }
  alpha=1-level
  z_a=qnorm(1-alpha/2)
  cat("The sample mean is", barx,", sample standard deviation is", s, ", and sample size is", n,"\n")
  cat("A large-sample confidence interval for the population mean with confidence level of approximately", level*100, "% is [", barx-z_a*s/sqrt(n),",",barx+z_a*s/sqrt(n),"]","\n")
  z_a=qnorm(1-alpha)
  cat("A large-sample upper-confidence bound for the population mean with confidence level of approximately", level*100, "% is", barx+z_a*s/sqrt(n),"\n")
  cat("A large-sample lower-confidence bound for the population mean with confidence level of approximately", level*100, "% is", barx-z_a*s/sqrt(n),"\n")
}

Tinterval=function(level=0.95,sample,n,barx,s)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(sample)==FALSE){
    n=length(sample)
    barx=mean(sample)
    s=sd(sample)
  }else if(missing(n)==TRUE | missing(barx)==TRUE | missing(s)==TRUE)
  {
    return("No sample was provided, please input the sample size/sample mean/sample standard deviation")
  }
  alpha=1-level
  t_a=t.quantile(df=n-1,1-alpha/2)
  cat("The sample mean is", barx,", sample standard deviation is", s, ", and sample size is", n,"\n")
  cat("A", level*100, "% two-sided confidence interval for the population mean is [", barx-t_a*s/sqrt(n),",",barx+t_a*s/sqrt(n),"]","\n")
  t_a=t.quantile(df=n-1,1-alpha)
  cat("A", level*100, "% upper-confidence bound for the population mean is", barx+t_a*s/sqrt(n),"\n")
  cat("A", level*100, "% lower-confidence bound for the population mean is", barx-t_a*s/sqrt(n),"\n")
}

Chi2interval=function(level=0.95,sample,n,s)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(sample)==FALSE){
    n=length(sample)
    s=sd(sample)
  }else if(missing(n)==TRUE | missing(s)==TRUE)
  {
    return("No sample was provided, please input the sample size/sample standard deviation")
  }
  alpha=1-level
  s2=s^2
  chi_a1=Chi2.quantile(df=n-1,1-alpha/2)
  chi_a2=Chi2.quantile(df=n-1,alpha/2)
  cat("The sample standard variance is", s2, "and sample size is", n,"\n")
  cat("A", level*100, "% two-sided confidence interval for the population variance is [", (n-1)*s2/chi_a1,",",(n-1)*s2/chi_a2,"]","\n")
  chi_a1=Chi2.quantile(df=n-1,1-alpha)
  chi_a2=Chi2.quantile(df=n-1,alpha)
  cat("A", level*100, "% upper-confidence bound for the population variance is", (n-1)*s2/chi_a2,"\n")
  cat("A", level*100, "% lower-confidence bound for the population variance is", (n-1)*s2/chi_a1,"\n","\n")

  chi_a1=Chi2.quantile(df=n-1,1-alpha/2)
  chi_a2=Chi2.quantile(df=n-1,alpha/2)
  cat("The sample standard deviation is", sqrt(s2), "and sample size is", n,"\n")
  cat("A", level*100, "% two-sided confidence interval for the population standard deviation is [", sqrt((n-1)*s2/chi_a1),",",sqrt((n-1)*s2/chi_a2),"]","\n")
  chi_a1=Chi2.quantile(df=n-1,1-alpha)
  chi_a2=Chi2.quantile(df=n-1,alpha)
  cat("A", level*100, "% upper-confidence bound for the population standard deviation is", sqrt((n-1)*s2/chi_a2),"\n")
  cat("A", level*100, "% lower-confidence bound for the population standard deviation is", sqrt((n-1)*s2/chi_a1),"\n")
}

Propinterval=function(level=0.95,n,X)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(n)==TRUE | missing(X)==TRUE)
  {
    return("No sample was provided, please input the sample size/the value of X")
  }
  if(X<5 | n-X<5){cat("Warning: Because either X or n-X is less than 5. The CLT might not work well, and the following results should be used with caution ")}
  p=X/n
  alpha=1-level
  z_a=qnorm(1-alpha/2)
  cat("The sample proportion is", p,"and sample size is", n,"\n")
  cat("A large-sample confidence interval for the population proportion with confidence level of approximately", level*100, "% is [", p-z_a*sqrt(p*(1-p)/n),",",p+z_a*sqrt(p*(1-p)/n),"]","\n")
  z_a=qnorm(1-alpha)
  cat("A large-sample upper-confidence bound for the population proportion with confidence level of approximately", level*100, "% is", p+z_a*sqrt(p*(1-p)/n),"\n")
  cat("A large-sample lower-confidence bound for the population proportion with confidence level of approximately", level*100, "% is", p-z_a*sqrt(p*(1-p)/n),"\n")
}

Predinterval=function(level=0.95,sample,n,barx,s)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(missing(sample)==FALSE){
    n=length(sample)
    barx=mean(sample)
    s=sd(sample)
  }else if(missing(n)==TRUE | missing(barx)==TRUE | missing(s)==TRUE)
  {
    return("No sample was provided, please input the sample size/sample mean/sample standard deviation")
  }
  alpha=1-level
  t_a=t.quantile(df=n-1,1-alpha/2)
  cat("The sample mean is", barx,", sample standard deviation is", s, ", and sample size is", n,"\n")
  cat("A", level*100, "% two-sided predict interval for the next observation is [", barx-t_a*s*sqrt(1+1/n),",",barx+t_a*s*sqrt(1+1/n),"]","\n")
  t_a=t.quantile(df=n-1,1-alpha)
  cat("A", level*100, "% upper-confidence bound for the next observation is", barx+t_a*s*sqrt(1+1/n),"\n")
  cat("A", level*100, "% lower-confidence bound for the next observation is", barx-t_a*s*sqrt(1+1/n),"\n")
}


sample.size.Zinterval=function(level=0.95,sigma,E)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  alpha=1-level
  z_a=qnorm(1-alpha/2)
  n=ceiling((z_a*sigma/E)^2)
  cat("In the estimation of mu, the samllest sample size to control the margin of error E <=", E, "at",level*100, "% confidence level is", n, "\n")
}


sample.size.Propinterval=function(level=0.95,ini.p=0.5,E)
{
  if(level>=1|level<=0){return("the confidence level should be between 0 and 1!")}
  if(ini.p>=1|level<=0){return("the initial estimate should be between 0 and 1!")}
  n=ceiling((qnorm(1-(1-level)/2)/E)^2*ini.p*(1-ini.p))
  cat("In the estimation of p, the samllest sample size to control the margin of error E <=", E, "at",level*100, "% confidence level is", n, "\n")
}