Tests a sample from a normally distributed population with a known standard deviation to determine if the hypothesis that the population mean has a specified value should be accepted or rejected.

Syntax

reject, p_value, conf = ZTest(data, mu, sigma, alpha)

Arguments

Name

Description

data

A vector containing sample data.

mu

The hypothesized population mean to be tested.

sigma

The known population standard deviation.

alpha

(optional)

The level of significance for the test, also known as the probability of a Type I error.  It must be in the interval (0, 0.5).  The default value is 0.05.

Outputs

Name

Description

reject

A Boolean value that is true if the hypothesis is to be rejected.

p_value

The largest value of alpha for which the hypothesis is to be accepted.

conf

A 100(1-alpha)% confidence interval for the population mean.  A two-element vector containing the lower and upper bounds of the interval, respectively.

Example

Test the hypothesis that a population with a standard deviation of 1.5 and a mean (mu) of 4 based on a sample of [2, 3, 5, 7, 4].

Syntax

reject, p_value, conf = ZTest([2, 3, 5, 7, 4], 4, 1.5)

Result

reject = false

p_value = 0.76559

conf = [2.8852    5.5148]