# Functions written in class on January 14, 2019

mymean <- function(x, remove.NA=TRUE)
{
  # A simple function to calculate the mean of
  # a vector. 
  # By default, missing values are removed.
  #
  if (remove.NA) 
    x <- x[!is.na(x)]
  if (length(x)==0)
    stop("No non-missing data provided")
  if (!is.numeric(x))
    stop("x must be numeric")
  sum(x)/length(x)
}

z.interval <- function(x, alpha=0.05, sigma=1) {
  # Calculate Z interval for the mean of a norma
  # population with known standard deviation sigma
  # 
  # Arguments: x - a vector of data
  # alpha - the significance level (default 0.05)
  # sigma - the population standard deviation (default 1)
  
  if (sigma<=0) stop("sigma should be positive")
  if ((alpha <=0)||(alpha>=1)) 
    stop("alpha should be in the interval (0,1)")
  xbar <- mymean(x)
  n <- length(x)
  z <- qnorm(1-alpha/2)
  ci <- xbar+c(-1,1)*z*sigma/sqrt(n)
  print(ci)
  ci
}