 Since the "standard" z-test is not available in R as in most real-world scenarios you're only ever going to use a t-test, this function fills that gap for teaching purposes. The function is basically a carbon-copy of stats::t.test, but with user-supplied variances for x and y and p-value and related calculations use a standard normal distribution.

z.test(x, y = NULL, alternative = c("two.sided", "less", "greater"),
mu = 0, sigma_x, sigma_y = NULL, paired = FALSE,
conf.level = 0.95)

## Arguments

x A (non-empty) numeric vector of data values An optional (non-empty) numeric vector of data values. A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter. A number indicating the true value of the mean (or difference in means if you are performing a two sample test). The assumed known variance of x and y. Must be numeric. A logical indicating whether you want a paired t-test. Confidence level of the interval.

## Source

t.test from the stats package.

## Value

An object of class htest, see stats::t.test

## Examples

x <- rnorm(10, 5, 1)
y <- 1:10 + rnorm(10, 3, 1.5)

# Two sample
z.test(x, y, sigma_x = 1, sigma_y = 1.5)#>
#> 	Two Sample z-test
#>
#> data:  x and y
#> z = -6.9144, df = 18, p-value = 4.698e-12
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -4.437182 -2.477218
#> sample estimates:
#> mean of x mean of y
#>  5.110855  8.568055
#>
# One sample
z.test(x, sigma_x = 1, mu = 5)#>
#> 	One Sample z-test
#>
#> data:  x
#> z = 0.35055, df = 9, p-value = 0.7259
#> alternative hypothesis: true mean is not equal to 5
#> 95 percent confidence interval:
#>  4.49106 5.73065
#> sample estimates:
#> mean of x
#>  5.110855
#>