Hypotheses

H_{0}: p_{1} ≥ = ≤ p_{2}

H_{1}: p_{1} < ≠ > p_{2}

Test statistic

Normal distribution

__Sample data__

validation message

Binomical distribution - the probability for event within each group is identical | |

Expected difference d between the populations's average is known |

p_{1}, p_{2} the sample probabilities or x_{1}, x_{2} the number of successes | |

n_{1},n_{2} - Sample size of group1 and group2 |

The following R code should produce the same results:

The prop.test uses the Chi-squared statistic with one degree of freedom, which is **exactly** as using the Z test: z^{2}=χ^{2}(1)