Hypothesis Testing for Proportions

A learning component on hypothesis tests for a population proportion.

Options

types | array<string>: the type(s) of test (One-Sample, Two-Sample) the widget should expose. Default: [ 'One-Sample', 'Two-Sample' ].
feedback | boolean: controls whether to display feedback buttons. Default: false.
nullHypothesisAsValue | boolean: always display the null hypothesis as a single value. 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

<LearnProportionTest />

<LearnProportionTest />

Result

Hypothesized proportion (null hypothesis):

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

Sample proportion:

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} : p = 0.5 v s . H_{1} : p \neq 0.5

H_{0} : p \leq 0.5 v s . H_{1} : p > 0.5

H_{0} : p \geq 0.5 v s . H_{1} : p < 0.5

We calculate the following test statistic:

z test-statistic = \frac{\hat{p} - p}{\sqrt{p (1 - p) / n}}

Plugging in our values, we have:

z = \frac{0 - 0.5}{\sqrt{\frac{(0.5) (0.5)}{5}}} = - 2.236

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

P (| Z | > 2.236) = 0.025