CIpilen_data: Confidence Interval and Sample Size for the Population...

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

Confidence Interval and Sample Size for the Population Proportion

Description

Data generation for the necessary sample size of a confidence interval, for the population proportion, using z^2/l^2). Either the estimation error e or the length of the interval l must be given (l=2*e). It is ensured that the computed p deviates from pi.

Usage

CIpilen_data(
  pi,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

dcipilen(
  pi,
  e = NULL,
  l = NULL,
  conf.level = c(0.9, 0.95, 0.99),
  nmin = 30,
  size = NA,
  u = c(seq(0.1, 0.4, 0.001), seq(0.6, 0.9, 0.001)),
  full = FALSE
)

Arguments

pi	numeric: vector of possible population proportions
e	numeric: vector of estimation errors
l	numeric: vector of lengths of the interval
conf.level	numeric: vector of confidence levels of the interval (default: c(0.9, 0.95, 0.99))
nmin	numeric: minimal value of necessary observation (default: 30)
size	numeric: sample size for computing a sample standard deviation. Default NA means that the solution of the estimation is used
u	numeric: vector of quantiles used to sample the sample standard deviation (default: c(seq(0.15, 0.45, 0.001), seq(0.55, 0.85, 0.001)))
full	logical: if TRUE then a data frame with possible solution is returned, otherwise a list with a randomly chosen solution is returned (default: FALSE)

Value

A data frame or a list with:

• e estimation error

• pi population proportion

• conf.level confidence level

• l interval length

• x 1-alpha/2

• q z_{1-alpha/2}

• q2 z^2_{1-alpha/2}

• n computed minimal sample size

• N the smallest integer, no less than n

• p sample proportion

Examples

# one solution
CIpilen_data((1:9/10), (1:9)/10)
# all solutions
pil <- CIpilen_data((1:9/10), (1:9)/10, full=TRUE)
str(pil)

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