# chickadee » statistics » z-test

##### Identifier search
(z-test x-bar n #:mu #:sigma #:tails)procedure

Given x-bar the sample mean, n the number in the sample, #:mu the distribution mean (defaults to 0), #:sigma the distribution standard deviation (defaults to 1), and #:tails the significance to report on:

• ':both, the probability of the difference between x-bar and #:mu
• ':positive, the probability that observation is >= x-bar
• ':negative, the probability that observation is <= x-bar

e.g. given a distribution with mean 50 and standard deviation 10

```; probability that a single observation is <= 40
> (z-test 40 1 #:mu 50 #:sigma 10 #:tails ':negative)
0.158655
; probability that 10 observations are <= 40
> (z-test 40 10 #:mu 50 #:sigma 10 #:tails ':negative)
0.000783
; probability that 5 observations give a mean of 40
> (z-test 40 5 #:mu 50 #:sigma 10)
0.025347```