Population Proportion Interval

## Description

Here, we will generate a confidence interval for a population proportion using the formula

(1)
\begin{align} \hat{p}\pm z^* \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \end{align}

where $\hat{p}$ is the sample proportion, $n$ is the sample size and $z^*$ is the positive z-score corresponding to the desired confidence level.

## Sage Cell

Note that paste is used to return the results, not print. In R, print is a difficult to use generic function, and so paste can be used for intuitive, python-style printing.

#### Code

n <- 200
phat <- .62
conflevel <- .95
zstar <- qnorm(conflevel + (1 - conflevel)/2)

lower <- phat - zstar * sqrt((phat * (1 - phat))/n)
upper <- phat + zstar * sqrt((phat * (1 - phat))/n)
paste("(", lower, " , ", upper, ")")


## Options

#### Defining a function for generating a confidence interval

Using the function method, we can define a function to generate a confidence interval for a population proportion.

#### Code

propInterval <- function(n, phat, conf.level) {
zstar <- qnorm(conf.level + (1 - conf.level)/2)
lower <- phat - zstar * sqrt((phat * (1 - phat))/n)
upper <- phat + zstar * sqrt((phat * (1 - phat))/n)
return(c(lower, upper))
}

propInterval(200, .62, .95)


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