exams.forge (version 1.0.10)

CIpilen_data: 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
)

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

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)

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)