R/417_Functions.R

In loganbradley/Loganstat:

library("roxygen2")
library("devtools")


# I will  start by creating some functions for different types of confidence intervals

#' A two-sided confidence interval with a known variance 
#' 
#' @param mu (what we believe to be) the true population mean
#' @param xbar the sample mean of the data
#' @param confidenceLevel the significance level for the CI, i.e., 1 - alpha
#' @param variance the *known* variance of the data
#' @param n the number of data entries
#' @return returns a test statistic,  a p-value, and a confidence interval consisting of lower and upper bounds
z_ci_sigma <- function(mu, xbar, confidenceLevel, variance, n) {
  testStatistic <- (xbar - mu) / sqrt(variance / n)
  pValue <- 2 * pnorm(- abs(testStatistic) )
  lowerBound <- xbar + qnorm( (1 - confidenceLevel) / 2) * sqrt(variance / n)
  upperBound <- xbar - qnorm( (1 - confidenceLevel) / 2) * sqrt(variance / n)
  cbind(testStatistic, pValue,  lowerBound, upperBound)
}