exams.forge (version 1.0.11)

CImu_data: Confidence Intervals for a Population Mean

Description

Computes confidence intervals for a population mean (mu) using either supplied data or data generated from a normal distribution with specified parameters. The function calculates key statistics such as the sample mean, standard deviation, and confidence intervals at user-defined confidence levels. Results are returned as a structured list containing observed and/or theoretical values, interval endpoints, and related measures.

Usage

CImu_data(
  x = NULL,
  n = length(x),
  xbar = NULL,
  sd = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  mu = NULL,
  sigma = NULL
)
dcimu(
  x = NULL,
  n = length(x),
  xbar = NULL,
  sd = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  mu = NULL,
  sigma = NULL
)

Value

A list containing:

a

upper-tail probability 1 - (1 - conf.level) / 2

n

sample size

xbar

sample mean

mu

theoretical mean (if provided)

sd

sample standard deviation

sigma

theoretical standard deviation (if provided)

df

degrees of freedom (if using a t distribution)

q

critical value(s) from the normal or t distribution

ss

standard deviation used in calculations (sd or sigma)

e

margin of error (half-width of the interval)

l

interval length

v

confidence interval endpoints

Arguments

x

numeric vector of observed data. If NULL, data are simulated.

n

integer: sample size (if n < 1, defaults to 5).

xbar

numeric: sample mean (computed from x if NULL).

sd

numeric: sample standard deviation (computed from x if NULL).

conf.level

numeric vector of confidence levels (default: c(0.9, 0.95, 0.99)).

mu

numeric: true population mean (used for simulation if x is NULL).

sigma

numeric: population standard deviation(s) (used for simulation if x is NULL).

Examples

# Using observed data
x <- rnorm(100)
CImu_data(x, conf.level = 0.95)

# Simulating data internally
CImu_data(n = 100, conf.level = 0.95, mu = 0, sigma = 1)