CImu_data: Confidence Intervals for a Population Mean

In exams.forge: Support for Compiling Examination Tasks using the 'exams' Package

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
)

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).

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

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)

exams.forge documentation built on Aug. 21, 2025, 5:41 p.m.