#' @title P-value for proposed mean of a population (known sigma)
#' @description Calculates the p-value for a proposed mean for a population with known standard deviation, using the Z-statistic (normal distribution).
#' @param x Sample mean
#' @param sig Population standard deviation
#' @param n Sample size
#' @param mu Population mean
#' @param side To either get a two-tail or one-tail p-value (Default is "two")
#' @export
#' @return P-value
#' @examples
#' x <- 2.6
#' sig <- 0.3
#' n <- 36
#' mu <- 2.5
#' pval_z(x, sig, n, mu)
#'
pval_z = function(x, sig, n, mu = 0, side = c("two", "one")) {
z = (x - mu) / (sig/sqrt(n))
pval = stats::pnorm(abs(z), lower.tail = F) * 2
if (any(side == "two")) {
pval = (signif(pval, 3))
} else {
pval = signif(pval/2, 3)
}
return(pval)
}
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