Hypothesis Testing for Means

A learning component on hypothesis tests for a population mean.

Options

types | array<string>: the type(s) of test (One-Sample, Two-Sample) the widget should expose. Default: [ 'One-Sample', 'Two-Sample' ].
tests | array<string>: the test(s) exposed by the widget. Default: [ 'Z-Test', 'T-Test' ].
nullHypothesisAsValue | boolean: always display the null hypothesis as a single value. Default: false.
feedback | boolean: controls whether to display feedback buttons. Default: false.
pValue | string: custom label for the p-value (should be a LaTeX equation string). Default: none.
style | object: CSS inline styles. Default: {}.

Live Editor

<LearnMeanTest />

<LearnMeanTest />

Result

Hypothesized mean (null hypothesis):

Let's assume that we have observed data with the following characteristics:

Sample mean:

Sigma

(σ)

Sample size:

We conduct the following test (click on the hypotheses below to switch between the one-sided variants and the two-sided test):

H_{0} : μ = 0 v s . H_{1} : μ \neq 0

H_{0} : μ \leq 0 v s . H_{1} : μ > 0

H_{0} : μ \geq 0 v s . H_{1} : μ < 0

We calculate the following test statistic:

z Test Statistic = \frac{\bar{x} - μ}{σ / \sqrt{n}}

Plugging in our values, we have:

z = \frac{0 - 0}{1 / \sqrt{5}} = 0

Under the null hypothesis, we calculate the p-value:

P (| Z | > 0) = 1